I have played about 20 games with Fizz, I loved him so much I decided to make a build for him.
He scales very well with AP and if you play him correctly you can get FB and have the jump start to kill!
Remember that E is your main ability and Sheen is your item to rush. after that you can pretty much just take some survivability items.

For Runes I Chose Magic pen and tones of AP, you can sub out the mana regen ones if you feel you don't need them,CD reduction would be a lot better. I put them in just because early game you can become OOM easy. If you are smart with your abilities early on you will not need it, and late game you dont need it at all.

I went With a Hybrid-ish build with these, straight for the CD reduction, you miss out on the last ability on the green tree, but I like the magic pen better with the buff for ignite/exhaust and also the point in turret damage. you are straight AP and its difficult to build into magic pen with the items you will need.
If you want the extra boost for your summoner abilities then go for it, its all about preference.

Lich Bane Lich Bane Lich Bane Lich Bane Lich Bane Lich Bane
this is your key item, you use it to burst harass then GTFO


I start with the Amplifying Tome and work it into a Sheen then I go for my Ionian Boots of Lucidity
depending on how many kills I have or gold I have or if i am getting owned... if everything is going ok (low death count for my team) I will try and finish off Lich Bane.
after you get your lich bane, you can become way more aggressive.

If you need the survivability Rod of Ages works really well with fizz. you can lane better and not die as fast

Rabadon's Deathcap is amazing because fizz scales so well with AP, but only take this if you know you can survive with out defense, Rylai's Crystal Scepter works well for chasing because your basic attacks will put magic damage on the target.
honestly after you get lich bane you can dominate, just make sure you watch the other team because as the game goes on you will become less effective if you are not careful! I found that I do really well when I get lich bane but like 10 minutes after that I will start to lose my firepower and wont be able to outlast anyone, so defensive items are key.

if you are already ahead and winning and just need some way to stay in lane, then take Will of the Ancients use an E ability in the center of a minion mave about 2-3 times and you should be good to go.
try not to build a Void Staff that item is for strict AP and does not go toward your survivability items, let a mage take it if necessary

Sorcerer's Shoes are good, They can totally be picked over lucidity, I just prefer the CD because with your masteries and the boots it comes to 25%

Frozen Mallet good survivability, but remember he is AP not AD so dont get this, if you need to chase then take the crystal scepter.

Abyssal Mask this is pretty good if they are starting build MR its like a deathcap in a way, good survivability but only against AP so it isn't too bad. I take this if they are heavy AP and are building against you

Deathfire Grasp this is very very good. I love this item!!!! remember to open with it. if you are one of those people who forgets that they even have items and doesn't use them... then you need to learn how to use them and this is the reason why. I mean right off the bat take out 30% of their health... you can pretty much kill them at full health with this item. The thing is, its hard to build so you may need to have some survivable item before this, but this is a good thing to get. I still prioritize Lich Bane over this item! this is good if they are high HP champs, I might take the bloodrazor over this depending on how early the game is.

Madred's Bloodrazor I have tried this item a few times. I dont need the Attack speed too much, but the fast that it takes their Hp away? this item plus your poison is sooo much damage! it is a nice pick if they are high health opponents.

Nashor's Tooth I like this for the AP and the CD reduction. I dont need the mana or the attack speed. So i feel like I am paying too much for this item, It is a good item but I want to focus on surviving and doing AP damage

Hextech Gunblade ok I have tried this item out a lot, I have tried to incorporate it into the build. I tried building the spell vamp part of it first, I tried building the life steal part first. It just doesn't work with fizz, I get killed every single time I build this item. It cost too much and he doesn't really survive that long to use the life steal and spell vamp. He scales better with spell vamp but getting straight health is way more useful and going back to spawn every once in a while to heal is way more efficient.

Start with your Playful / Trickster This is your main ability abuse the @#%& out of it.
This is really good for early gank first blood, because it gets you out of the situation if you are focused so your team can move in and kill, or good for the final chase. DO NOT initiate with this spell EVER unless they are low and you are guaranteed a kill. in the early game this is your only way of evading or running so use it wisely at the start of the game.
During mid game you can use this ability to chase, run, and evade almost every skill shot there is (if timed right). it will take some skill to get used to the timing, but the basic way the ability works is this-
once you hit E you jump to the direction of where your curser is at, kind of like flash (except it takes about a second and you are immune and un-targetable throughout the whole thing). Then if you do nothing after the whole jump flippy thing you slam the ground in a pretty large area doing a good amount of AoE damage and putting on a tiny slow. hitting the button a second time activates the second ability which makes fizz jump a second time (a smaller distance) and slams the ground where he lands. the bad part about the second ability is that it will not slow the enemy and the radius is drastically smaller where he hits, so make sure you only activate the second ability if you are running or far away and chasing someone, because chances are you can hit them with your slow effect with the first part because the radius is pretty large. if you do decide to activate the second ability you need to react pretty quickly the exact timing is .75 seconds but if you are human then just spam the button....
(take this advice lightly, It works in 3 on dragon, not in 3 spawn and over a few small walls on both 3's and 5's) One cool part about this is that you can jump over most walls with it, which can drastically improve survivability when running away from champs. I found that you may need to use the second part of the ability to jump over a wall ( I dont know why that is... seeing is that the second jump is a shorter distance, but it will sometimes register weird and only put you over the wall on the second jump.

Seastone Trident This poison damage will add up very quick so apply a hit every once in a while, remember you are very squishy especially during early laning phase so try not to let them damage you more than you do to them. the poison is based on missing health, so as they get lower health try applying for hits and pushing them. You only need one hit every 5 seconds, dont just rush into them and try and duke it out, Hit them with your Q/E and get out of there. Your Q ability applies this poison so you dont need to actually hit them, just dash in and run away.

Urchin Strike this ability allows you to apply your poison on them quickly and use your playful/trickster to jump out of there. The main damage from this ability comes from your Sheen or Lich Bane and AP, so dont worry about leveling it until late game. REMEMBER!- this ability makes you move in 1 direction the same distance no matter what. so it is your main juke ability! it can turn against you if you use it too close to an enemy you will end up somewhere odd like behind them in THEIR turret. this move combos with your E ability. Rush in and hit them with your 'on hit effect' part of this ability and then trickster your butt out of there. Once you get skilled, (in a 1v1 lane) you can trickster behind the enemy and do splash damage to them and their minion, then position yourself so that your urchin strike dashes you through the enemy and into your side of the minion wave. It is tricky but if done right can take a big chunk of their health. let your poison tick them down before you apply another hit. your damage comes from the burst ap and damage over time, not the actual attack damage.

Take your ult Chum the Waters when you can
this ability is amazing. I have found that you should definatly open with this, it is not a finisher, unless you are helping someone else finish their enemy or chasing someone. The range on this ability is very big so dont underestimate it. also the CD is about a minute so you can use it "all day ery day"

ok Simple little guide to kill with fizz mid game.
So first you want to take into account the different ways to use your abilities that I have mentioned above in your 'skill sequence'. So just widdle them down with your poison by dashing in with your Q and trickster out. Then after they are about half health, let them push a little bit and use your ult. when it hits them, they will be slowed, that is when you dash over with your Q ability, then just wait until thay are knocked up in the air, after they take a ton of damage you take maybe 1 or 2 hits and use trickster right on top of them, when you crash down they will probably need like 2 more hits, remember by this time your Q will be off of CD, save it for if they decide to run away or for the finisher. If after all of that (using Q twice and your ult and an E) if after all of those thing, they are not dead.... you are focusing the wrong person.
If they are killing you before this, it is time to get some survivability items

This is very important, starts the whole game off in your favor (duh)
So you need to play very defensively until you get your 3 abilities, dont even think about getting a kill until then. Start with your playful/trickster ability, use it to dodge and farm, DO NOT PUSH THE LANE. last hit minions it is crucial. once you get your poison try and tag them and jump away with playful. once you get your urchin strike activate your seastone trident and dash in with your strike then playful out of there. do that a few times until they back off, (or if you are balsy enough pop your summner spells and finish the job. Let them tower dive you! with your playful ability they cant attack you so they just have to deal with your turret, just make sure they get the turret agro before you use it or else you have nothing to run away with.
AS SOON as you get your ult you pop it and go in for the kill. by that time you should have harrased them down enough so that you can kill them right then and there. (you should have used your potion by now as well.) when you kill them recall and get your sheen. follow the first part of this and get yourself another kill. get your boots and by this time they will learn how your tricks work. So back off and try not to get focused.

your main Goal is to take out the straggler champs, do not go into the middle of the fight regardless of how much AoE damage you do, that is not what that ability is for. SO dont do it, you are very squishy and have good burst so harass until they are low and then commit with your ult!

early game you need to take advantage of the passive he has, cut into the lane and poke the champs through their own minions

I have veiwed a lot of Fizz builds and I have found that ignite was not wanted at all! but remember - Fizz is not ranged! and that extra Ignite damage plus your trident ability is very helpful!

Exhaust is what I think personally is the best ability you can get. it is a slow-armor and magic res reducer- and they are pretty much weak as a soraka with no AP for 2 seconds!

If you dont like ignite then you can switch it up and take Ghost if you are comfortable with the need for chasing.

Flash was recently nerfed but it is a very viable pick, its like taking flash as ezreal it is useful but not neccesary. This is one of the best summoner abilities there is, I just like taking exhaust its personal preference.

Surge is very nice, it just gives you the extra boost you need, I would take ghost over this ability but if you are a more aggressive player then take this one

Teleport meh, good in 5 if you are a support but just take ghost if you need to get somewhere

Clairvoyance let a support take this

Cleanse not a bad pick, fizz can bee focused easy so this could help you get out of a bad situation if they have a lot of stuns. I would take flash over this but it is all situational.

Rally dont take this, fizz is AP not AD, if you want the boost just take surge.

Clarity nope, your are AP but you dont need this, you dont get mana problems, you recall before you run out of mana due to your lack of health

Heal They recently buffed heal, and putting a point in your masteries for this ability might make it pretty good. I have tried it a few times and it isnt bad at all. I just like to be more aggressive so I take offensive stuff instead.

Fortify this is a no... but it is really funny to see people turret dive you, pop this ability, use your ult and use your E ability to avoid them and see them die....... it isnt worth taking this though :P

Promote Revive Smite dont even know why i need to put this here. do not take

PRO
- he is amazing at 1v1 because of his poison
- can get around the map easily and evasively
- ult can be a game changer! breaks up team fights and can catch a far enemy runaway
- very nice harass around level 6-7 (thats when you can start to rack the kills

CON
- Squishy!!! lay low until you get your 3 abilities!
- late game you can be out matched in a 1v1 if you are not careful to watch what you build
- playful/trickster is your main evasion ability so make sure you dont waste it on the initiation, you may need it to bale!