Hey, I'm a pretty new player but I love playing Zoe and I've mained her the most. I would so recommend playing her for anyone that just loves a cute and playful champion. With her full combo, she has the capabilities to simply oneshot almost all adcs. Anyway, enjoy my first guide on zoe :)

Passive-
Her passive is like a buffed up lich bane. After you use an ability, you're next auto attack with deal extra magic damage. You'll mostly be using it when you want to simply deal that extra damage to finish someone or to proc dark harvest. However, it's also great to deal a ton of damage to turrets as they don't have magic resist or finishing minions. Once you get better, you can even use it to poke enemies with it.

Q-
Starting with her Q, this is her main ability. It is where you'll get most of your damage from. It increases in damage the further it travels so you'll mostly want to cast it behind you first then cast it forwards towards the enemy champion. You can also use this to finish casters after you've bought ludens as it will one shot them. Since your Q is cast twice, you can actually proc your passive twice which is great for dealing extra damage to turrets and finishing enemy champions.

W-
After you've unlocked your W, enemy minions will sometimes carry little bubbles on them. Killing those minions will drop a summoner spell or some active items. This is where you start to be very flexible with your use. If you pcik up an ignite, you can use it to finish the enemy champion. Or if you picked up a flash, you can use it to escape or give your Q that extra distance. This is what will seperate pro zoe players to noob zoe players.

E-
Your E is what really increases allows you to one shot the enemy. After an enemy is hit, they will fall asleep after one second and stay asleep for one second. If an allied attack (everything other than minions) hits that enemy, the they will wake up but take double damage up to a cap in true damage. Super powerful especially with your ability to increase its travel distance by letting it travel through walls.

R-
This is like the beautiful sweetner to your abilities. It allows you to portal to a certain location for 1 second before portaling you back. Super flexible and super underrated. You can dodge abilties with this, pick up summoner spells protected by enemies, give your Q/E extra distance, and poke enemies with it. It's a super versatile abilty that you'll use very often due to its short cooldown and amazing ability.

E>Q1>Q2>R>AA
This will be your most common combo. Generally, this is when the enemy is hit by your E but is too far for you to hit normally so you use your ult to add the distance.

E>R1>Q1>R2>Q2>AA
This is when they're close enough to hit with your Q but you ult backwards then Q to give your Q a lot more distance. (The R1 is when you use your first portal, R2 is when you're brought back from you portal. Note that R2 doesn't involve clicking anything)

E>Q1>Q2>R1>Flash>R2
This is when the enemy is super far from you and they've hit your E (happens if you E'ed through a wall or they hit the pool and you've left). This involves adding your flash into the mix. It's the same combo as your normal one but as you enter your first portal, you'll flash (Either through your own summoner or W) to give your Q more distance.