This is a bad build.

As waffl3x pointed out, Fizz apparently doesn't benefit from the 1% spell vamp in utility, so I took the point from Transmutation, one point from Good Hands, and put both of those points into Swiftness for 1.5% movement speed.

November 14th
Started adding dates to changelog. I've been doing different things with my Fizz play, and I'll be making changes to reflect that. First, I no longer rush GA and I'm VERY happy with the results. Sheen is now my first item goal, though I still start with Cloth Armor and health pots.

I play Fizz weird. I juke, I dodge, I wear them down, I use my taunt. Either I kill them, they run away frustrated, or my team swoops in to say hi.
I play with my enemies. I walk along them as they try to run away, I turret dive often, I tell them a joke, I attack wolves and run away. Basically, I troll.
This build is for me really, just for me. I will honestly be surprised if I ever see anyone use anything remotely similar to this build. The items themselves aren't bad, but the build order, definitely is.

These are the runes I got from a Gragas guide, they work for me. I prefer per level runes because I can play well enough early game that they pay off for me. I threw a flat rune in there for good measure though.

Also from a Gragas build. Works well enough.

There's no real sequence once you get a point in all of them. Sometimes I prefer the cooldown on my Playful/Trickster, sometimes I prefer the damage on Urchin Strike or Seastone Trident. Sometimes i get my ult at 6/11/16.

I use my spells a lot so Clarity is a personal must. You might like Revive.
Seriously though, if you don't have mana, you can't use your abilities. And for an ability power champion, that's like trying to drive a tractor with no gasoline. It helps early game and it helps late game.
Flash is there because you have a built in collision ignoring thing. You should have no problem escaping or catching up, but flash will help you do both better than ghost will. Use flash to get in range for Urchin Strike, hit a minion if you have to, use playful/trickster, to finally catch up. Or use flash to get away from a turret after you dive. Whatever, you might actually prefer ghost and it might be better for you.

The items are the main point of this build. I play Fizz as a very fun loving, playful, and above all SLIPPERY champion. Combined with his abilities, these items will make it nearly impossible for enemies to krill you. I start with cloth armor and health pots to stay in lane as long as possible. Generally it last me till level 6 or 7. Depending on who you're up against get either null-magic mantle or chainmail. Follow with basic boots. My first item is Sheen, which I later build into Lich Bane. Second, I'll buy Sorcerers Boots. Once you have GA, you can turret dive better, stay in team fights longer, bait enemies closer. It will give you a lot more options considering you have an extra life.
After GA and Sorcerers Boots, I get another chainmail armor and build Phantom Hourglass. Don't forget to move to the first slot so you can easily use, and don't forget to use it. I constantly forget I even have it and die when I could have gone into stasis, used q to get out of attack range, and hop away.
With those three items, you'll be invinseable. But you'll be only be dealing minor damage. You'll still hurt them, get a few kills, and you can still win the game with those three items. I often barely even get Hourglass.
Hextech Gunblade will give you ap, ad, life steal, spell vamp, and a powerful ranged slow. You go from just being unkillable to unescapeable. Or inescapable.
From here, it gets more situational depending on team comp. Try archangels staff, Rabadons Deathcap, add a pair of boots of swiftness, Abyssal Scepter, Void Staff, Item Finder, or Haunting Guise.

Low on Health? Use Urchin Strike to go through enemies, land in bush, Playful/Trickster over them and run the opposite way. They may chase. Just Urchin Strike back through them and P/T even farther away.

Not sure if ult will hit? Get closer. It's easy with Urchin Strike, P/T, and Flash.

Turret diving? Activate playful to lose all turret aggro.

Turret diving? Zhonya's loses turret aggro too.

Turret diving? Let your Guardian Angel revive you and you'll have lost all turret aggro.

Yeah, don't forget to use Zhonya's once you get it.

Use Playful/Trickster to dodge Ashe's ult, Karthus's Ult, Caitlyn's ult, and Fizz's ult. Just time it right or you'll still take the damage.

If you have any more questions, leave a comment. I'm really really looking for more discussion over this build, particularly the items. I may eventually decide to look over the masteries and rune page and feedback will definitely help. I'm not the best player, I hardly call myself a good player even when my friends say I am. They suggested I write this guide in the first place really but here it is, tell me what you think.
Again it fits my personal play style and I doubt anyone else would build this, but I would love feedback, particularly over masteries and runes.