Zoe is alot of fun to play for me. But she is also real hard. You have to aim well or you'll be in trouble. Use her mostly for tricky kills, like hiding in jungle using Sleepy Trouble Bubble and Paddle Star + Portal Jump is great to take out an enemy in group. Use your R commonly on enemies to activate dark harvest or pushing. At the start Mana will be very important. You can also bait your enemy by going to side bushes, watch them and aim your Sleepy Trouble Bubble.
Here is some moments of me playing her, I'll put more too.

I'll add more info int time about new items and other stuff.

Play Video Play Video

Strong Points:

[*] Damage Output: At level 2, she can have great trades if she manages to land her E + Q combo. With a AA + Q2 + AA combo, you can proc. Electrocute and deal good damage to enemy laner. And after get fed, she will be a nightmare for all squishy enemies.

[*] Spell Shards: With enough luck, Zoe's Spell Thief ability is really usefull. In laning phase, getting an extra Ignite or getting a Hextech Rocketbelt will help you kill your enemy or let you push. Her E + Q combo is what people really get annoyed, but her W is never should be underestimated. It gives movement speed and deals damage. Also makes it nearly impossible to escape from Zoe.

[*] Range: With good vision around the map, it makes dangerous to go around walls for enemy team. And also it helps to ganking, an over extended enemy will be an easy pick for Zoe. In addition, her Portal Jump lets her kill/farm from a safe distance. This also makes it possible to steal Drakes/Baron.

[*] Dodging Skillshots: Her Portal Jump can be used for dodging some dangerous skillshots. Also the movement speed she gains from her W will help you move around.

Weak Points:

[*] High Skill Cap: You need good aim and prediction to play her. Her main damage source and main CC cource are both skillshots. Especially in the laning phase, you can't use your Sleepy Trouble Bubble without caution. Or you'll be vulnerable. In team fights, it becomes a lot harder to land your skill shots. Because an enemy you don't aim can get in the way.

[*] Squishy: Even when ahead, an assassin can kill Zoe easily. After the laning phase, you need to play carefully, cause she is not really a 1v1 champ, especially against burst/all in champions.

[*] Teammate Who are unaware of Zoe/careless: It ruins your day when someone AA's a sleeping enemy. Your teammate must wait to attack/use their abilities, or you can lose an easy pick. Tell them to attack, after the enemy wakes up. Make sure you don't tilt them in the prosses.

[*] Spell Shards: The reason I put this in both Strong and Weak Points is, RNG. You can have great spells but it might give you something you don't need at that moment. Also if you have no Spell Shards, you have 1 less ability.

[*] Low mobility: The only thing that gives Zoe mobility is her W and that relies on use of summs or spell shards. Other than that she has no escape tool.

[*] Blocking Her CC/Damage: Her E can be easily countered. Like: Quicksilver Sash, Banshee's Veil, Wind Wall, Black Shield, Cleanse and more. Her Q can be body blocked too, champions like Braum can do this easily.

[*] Tanks: It becomes harder for Zoe to kill champion which has high magic resist. I especially hate when they have Spirit Visage. It heals a lot and has good MR. Grievous Wounds aren't really effective and you need to scale well in order to get some Magic Penetration.

: I use this rune against mages, mostly. It's early damage is good and thus making trades to your advantage.
Some Combos for procing Electrocute:
- Sleepy Trouble Bubble + Paddle Star + Paddle Star + More Sparkles! Play Video
- Paddle Star + More Sparkles! + Paddle Star + More Sparkles! Play Video
- Paddle Star + Paddle Star + More Sparkles! + Portal Jump + More Sparkles! Play Video
- Portal Jump + More Sparkles! + Sleepy Trouble Bubble + Paddle Star + Paddle Star Play Video
- Paddle Star + Paddle Star + Portal Jump + More Sparkles! + Sleepy Trouble Bubble Play Video
: This rune is good for poking melee champions early game, however you will give up on some damage that Electrocute would have deal.

: Easier to proc compared to Electrocute when enemies are on low health and synergizes with her More Sparkles!, Paddle Star and with Lich Bane. However, the damage is not high early. To be able to collect some souls, you need to gank a lot and make sure to kill or assist to reset its timer. Different than Electrocute, this rune can be used for cathing enemies on low health with Portal Jump.

Slot 1:

: If you can do a lot of Sleepy Trouble Bubble + Paddle Star combos, this choise is good for you.

: If you want sustain in laning phase while poking, Taste of Blood will suit you.

: If you can do a lot of Portal Jump + Paddle Star/ Sleepy Trouble Bubble combos, more than E + Q, this choice is good for you.

Slot 2:

: This choice is good for roaming with Control Ward and Oracle Lens. That way you can deny enemy vision and provide vision for you and your team mates.

: This choice is good for laning phase cause it provides longer vision for you. Also, Ghost Poro will alert you with alert you, so if you lose focus on the map, it might keep you safe. But be carefull, enemies can avoid them easily.

: I prefer this rune over others. They provide you extra tool but it is easier to gain the AP bonus with this.

Slot 3:

: This rune will help you keep sustain, especially after an E + Q combo.

: Not ideal for Zoe. If you go Everfrost or Hextech Rocketbelt on her, it will be kinda usefull, with the addition of reducing trinket CD. But you will have to give up sustain/roaming potential which, I don't recommend.

: Very good for roaming.

: Not recommened. You don't really need extra CD on your ultimate. Even if you have all stack, it will decrease the CD by just 2.75 seconds, which in my opinion, not worth.

Slot 1:

: Good against AP Mages like Diana, Fizz. This rune might help you survive fights.

: Good in early but wouldn't really recommend it. After getting Luden's Tempest, mana sustain never was a problem for me. But this rune might help you lane against other mages.

: Very usefull. Since you can use 4 or 5 times more summoner spells than other champions, Nimbus Cloak fill fit Zoe perfectly. In laning phase, if you get a spell shard from the minions, it will help you to run over and even land a Sleepy Trouble Bubble.

Slot 2:

: After the CDR changes, it is kinda get harder to have enough CDR or AH in this case. Especially if you build Luden's Tempest. So it is better to pick this choice for good AH. Also after level 11, this choice will help you to spam your abilities a lot.

: Synergizes Nimbus Cloak, but wouldn't really recommend it.

: Good in a lot of situations, laning phase and team fights. Since you are a squishy champion, you will most likely fight from a little distance and stay healthy.

Slot 3:

:This rune saved me a lot of kills, so it is good to have some extra damage. Also helps laning phase.

: A good choice. It could be usefull when you are with your jungler and in Drake fights.

:This is a late game choice, but Zoe isn't really strong in late game, so it is better to pick other 2 choices.

:I would use this rune against Zed. You can't really use it when he is level 6, but at least you can focus on building other items.

:A choise against good wave pusher, it will help you to prevent them shoving wave under your turret and roam.

:Use it against hard matchups and against laners that you need mana sustain.

:Usefull for trades. Getting immediate health and movement speed. Highly recommend it if you also have Biscuit Delivery.

: Most usefull sum. for Zoe. It will help you secru kills in laning phase. You can also use this spells in a situation where you are so close to die to proc Nimbus Cloak (If you don't have Flash). Also while fighting, you can use this spell early to kite around enemy, proc Spell Thief and collect other shards if there are any.

: If you are up against Lux or Neeko, this spell will come handy to escape their combo. In addition, if they also use ignite, you can take it and cleanse it.

: I would use it against heavy burst damages like Vel'Koz's.

: This spell is usefull against ***ains when they dive to you. Like Talon, Yasuo, Katarina. It will decrease their damage also make it easier for you to land a Sleepy Trouble Bubble. Note: Take this over Ignite if the matchup is too hard for you.

MORE SPARKLES!:

After casting an ability, Zoe's next basic attack or bubble within 5 seconds deals 16-130 (based on level) (+20% of ability power) bonus magic damage.

Zoe's passive is really important in many scenarios.
-Farming: It makes it easier to kill creeps since it has faster to cast and has more damage.
-Harras: After hitting the enemy champion or minions with Paddle Star, it gives you a easy chance to harras your enemy. Also More Sparkles! makes it easier to proc Electrocute.
-Hitting Sleeping Targets: If you happen to miss a Q, you can still AA to a sleeping enemy cause it will still deal good damage.
More Sparkles! is also really good with Lich Bane and Dark Harvest.

PADDLE STAR:

Zoe hurls a star in the target direction that collides with the first enemy hit, dealing 18-140 (based on level) (+ 50 / 80 / 110 / 140 / 170) (+60% of ability power) magic damage and 80% of that damage in a small area. Paddle Star's base damage is increased by 7-50 (at levels 1-18). The total damage is also increased by up to 150% based on distance traveled.

If the star does not collide with an enemy, it remains stationary for up to 1 second. Zoe can reactivate Paddle Star at any point to redirect the star to a new location near her, albeit resetting the current damage modifier.

Both the initial cast and reactivation will prime More Sparkles!.

Range: 800

Cooldown: 8.5 / 8 / 7.5 / 7 / 6.5

Cost: 50 / 55 / 60 / 65 / 70

Her main source of damage, harras and farming. It is important to position your Q well. Not just sending it back and forward, sometimes send it sideways to harras among minions. Timing the cast time of this ability is important for extra range. Like:
-Cast it, walk and right before the time ends, cast it again.
-Use Paddle Star, walk, use Paddle Star again and when it gets closer to you, use Portal Jump.

SPELL THIEF:

Passive - Spell Thief: Whenever enemy champions cast a summoner spell or item active, they drop the corresponding Spell Shard onto the ground. Spell Shards last for 40 seconds. Some enemy minions spawn with random Spell Shards that only drop to the ground if killed by Zoe. Spell Shards from minions last 20 seconds.

Collecting a Spell Shard allows Zoe to activate Spell Thief within the next 60 seconds, and she cannot pick up another Shard until she does.

Active: Zoe mimics the active of the collected Spell Shard.

Passive - Summoner Specialist: Casting Spell Thief or one of her own summoner spells grants Zoe 30 / 40 / 50 / 60 / 70% bonus movement speed as well as summoning three bubbles that orbit her for 2 / 2.25 / 2.5 / 2.75 / 3 seconds. The bubbles autonomously hurl themselves at nearest enemy, prioritizing her attack target, dealing 75 / 105 / 135 / 165 / 195 (+40% of ability power) magic damage per 3 bubbles.

Range: 550

Cooldown: 0.25

This ability never should be underestimated. Having 2 Ignites or an extra Barrier can change a fight with her. If you have a spell/item on your W, you can use it to run around and deal damage with the bubbles. It can be a lifesaver: pickind the Heal the enemy used or getting a Chilling Smite from the minions to steal a drake. If you have Minion Dematerializer, keep it for ballooned minions if possible. This ability is really good with Nimbus Cloak.

SLEEPY TROUBLE BUBBLE:

Zoe kicks a ball that detonates on the first enemy hit, dealing 60 / 100 / 140 / 180 / 220 (+40% of ability power) magic damage and making the target Drowsy, slowing them by 10 / 15 / 20 / 25 / 30%. After a brief delay, the Drowsy target falls asleep for 2.2 seconds.

Sleeping targets take double damage from the next attack or ability to hit them, up to a cap of Sleepy Trouble Bubble's damage, but are awoken early upon taking damage.

The ball's range is doubled when it passes through terrain. If the ball does not hit an enemy, it lingers on the ground as a trap for 4 seconds, which primes after a 0.8s delay.

Range: 800

Cooldown: 20 / 18.5 / 17 / 15.5 / 14

Cost: 80

Her one and only CC ability. Increasing your Paddle Star damage is what makes Zoe a one shot champion. Also extending the range with terrain causes nightmares for your enemies. Their effort of engage can be ruined by just one bubble. Having good vision is important for this ability too. You can take out a jungler who is waiting to gank you. Or you can block their roam, force them to leave drake/herald. The problem is, this ability can be countered easily. Cleanse, Banshee's Veil, Quicksilver Sash etc. So especially in early game, it is better to use this ability carefully. And against hard engage champions, it is better to not use this ability in most cases. Cause it will be a too risky play. If you miss, you'll have no defence and they will engage. Also make sure your teammates don't AA to sleeping target.

PORTAL JUMP:

Zoe targets a location and then dives into a portal that she opens beneath her, blinking to the target location after a very brief delay. After 1 second, she falls back through the portal and blinks back to her cast location.

Zoe remains able to attack and cast abilities during Portal Jump, and can see over walls, but cannot move.

Range: 575

Cooldown: 11 / 8 / 5

Cost: 50

Main reason for this ability is extending the range of Paddle Star or getting a good position to land a Sleepy Trouble Bubble. But there are other uses too:
-Picking spell shards.
-Catching enemies with More Sparkles!
-Dodging skill shots (Don't forget you can use it only for DODGING, not ESCAPING!)
-Vision (You can see behind the walls even behind them with this)
Carefull when using this ability, they can wait for you at your returning place or aim their skill shots there. Also point click abilities with stun can be dangerous too.

Play Video If you use your Portal Jump such as in this video, you'll be vulnerable to enemy CC and attacks.

STARTING ITEMS

I use this item against mostly other mages. It gives mana sustain and wave clear. Also can be used against other matchups, cause it gives 15 AP and it is usefull for Q poke.

I use this for melee matchups or if the lane is hard. It will help you keep sustain health, but the mana sustain is not as good as Doran's Ring. It is good with Time Warp Tonic. And it is also good with Summon Aery for poke damage. I you don't have 100% health or mana, you can use this before going trades or while just farming, cause even AA's will proc its DoT.

If you think it is an easy matchup and/or you can roam well, it is a really good start. You'll only need 350 gold to finish Corrupting Potion and they go really well with each other.

EARLY CORE ITEMS

It is better to focus on getting Lost Chapter as first recall item. There are a lot of reasons:
-CDR
-AP
-Flat mana
-Mana regen
This item will help you clear waves and also helps you stay in lane. And with its passive, you can look for roams after clearing lane if you get a level up.

The flat Magic Penetration is good. Also getting this item early will help you roam.

Good for early game Magic Penetration.

Good in early game against AD matchups.

CORE MYTHIC CHOICES

Things will change with these Mythic Items. However, the reason for you to build this item is not really changing. Good AP, good mana, good CDR... I mean Ability Haste and now decent Magic Penetration. Also it's Mythic Passive gives 5MP to all Legendary Items which is really great in damage means.

Now that this item has mana, instead of health, it became a really good option for Zoe. This item is good to deal with enemy teams that has tanks with high HP. Also, the Ability Haste this item provides is really good.

Compared to Luden's Tempest, stat wise, this item has only Health, instead of MP. Really good active for free Sleepy Trouble Bubble and good AP for other items.

Really usefull against burst damage.

OTHER MYTHIC CHOICES

Usefull active for shoving the wave or for extra range and mobility. It has better AP now. Also 5 MP is also a good point this item has.

Good AP, good Ability Haste. But the different part is your damage is increased for each second of combat and it has 15% Omnivamp, which is life steal for abilities. If you need a little more survivability you can use this item.

IMPORTANT ITEMS

Most important part about Lich Bane is that it's passive. Your More Sparkles! will deal good amount of damage that you can even use it to wake up your enemies. But I wouldn't recommend this item for your first item (Unless you are facing Yasuo. Because it's stats are lower than Luden's Tempest. Especially mana.

AP

Time your recalls well, cause it requires 1250 Gold for one rod. If you are doing great in game, you can rush this before Lich Bane.

Very important against tanks. Void Staff is better at mid/late game cause it has percentage Magic Penetration.

If they have champs with good sustain ( Darius, Fiddlesticks, Soraka etc.), this choice is good, but Grievous Wounds can't do much to a Darius with a Spirit Visage. So it is better to get Void Staff over Morellonomicon.

OTHER CHOICES

Very usefull for AD matchups. Also its active will help you dodge heavy burst ultimates like Zed's and Talon's.

Usefull if the enemy mid laner and/or enemy jungler has heavy CC.

If you are having a hard time against the enemy mid laner who is AP, it is a good choice. Also it will not block completely a CC like Banshee's Veil, but it will reduce the time of multiple CC.

If the enemy mid laner who is AD gets ahead, this choice will help you survive a bit more. It also reduces AA damage more so against champs like Lucian, this item is so usefull.

SITUATIONAL ITEM

This is a high risk high reward item. Consider this when you have stacks on your Dark Seal. I recommend this if your team has someone that can peel/protect you or if you can easily escape.

: If he lands his Bandage Toss, you will be mostlikely dead. He is excellent at locking someone. If he lands his Q on a minion, don't think you are safe and keep your distance as much as possible, cause his Curse of the Sad Mummy has good range and 1.5 stun at level 1.

: Pre 6, not a big problem. After 6, HUGE problem. When you are just peacefully farming or trading, a heart above your head will give you a heart attack. Even without her charm, she can delete you in no time. So it is better to play safe if you don't see her on the map and never forget control wards.

: He will mostly farm till 6 and ganking lanes with his ult. Make sure you have vision on the side you are close, so he can't fear you. Warding bushes is good but don't forget, he can come from other side of the walls.

: Pre 6, make sure he can't use his Alpha Strike on you.
So he can't be a threat to you. After 6, it is better to not encounter him, cause his Highlander will help him o catch you easily and he can dodger your abilities with his Alpha Strike. If you manage to use your Portal Jump at the right time, when he Q's on you, you can leave him behind a wall.

: Getting deep vision is important. If you just ward bushes, he will be too fast for you to react.

: He is played mostly at top lane (and rarely at sup), but this
advice will be valid for every role, because of his Stand United. It will be a very bad situation, cause he will probably his teammate and make the situation dangerous for you. If you are not 100% sure that you can kill the enemy before he arrives, leave immediately. Cause if he catches you with his Shadow Dash, you will mostlikely die.

: If you land your Sleepy Trouble Bubble on someone that Yuumi is attached, she can easily leave the person she is on and body block your E. It is better to wait for her to detach than use your Q from an angle she can't block.

: Similiar to Yuumi. He can block your Q. So you should look for a good angle to avoid him.

At first wave, you can cast your Paddle Star near your turret, then use it again to deal massive damage to melee minions. this way you can push the wave and harras enemy laner under their turret. But make sure you have vision or the enemy jungler can't kill you early. Other than harrasing, you can get deep vision or help your jungler while your enemy laner don't have prio. Check your bot lane often, cause roaming is Zoe's strong points. If your wave is in good position, you can go bot lane, help them kill enemy or pressure them for drake. After you are 6, you should look opportunities to use your Portal Jump and land a Sleepy Trouble Bubble. However, if the enemy can block your E ( Malzahar, Yasuo), or they can avoid it ( Zed), it is better to wait for them to engage/make a mistake. Cause if you don't have Sleepy Trouble Bubble, you are very vulnerable.

If the enemy has better wave clear and locking you under turret, make sure you notify your jungler. Even if you don't kill the enemy, it will help you farm safely and prevent them from roaming.