Fizz is a very interesting champion to work with, and has several routes open for building him due to his abilities. Therefore, let me first say that this build is not for everyone. Also, please try before you vote, and let me know how to make it better.

This build is based off of Fizz's "w", Seastone Trident, and its on-hit effects. Not only can it deal massive up-front damage as a passive, it also applies a DOT (damage over time) on any target it hits, while also providing an active for even further damage and reduce your targets' healing. Therefore, it is vital to learn how to control Fizz's attacks to hit each target once, then hitting the next, and cycling through them (only applies to hitting minions really, obviously in champion fights, you want to focus one at a time to take them down fast).

The masteries and runes both are to help maximize the damage potential of the DOT, by increasing both your AP and your attack speed, while the items help boost your AP, provide additional on-hit effects, and give you a bit of survivability and sustainability.

So, without further ado, I present to you, Fizz, The Tidal Trickster

PROS: great at early game harassment easy to get kills on runners (thanks to Seastone Trident) easy to get in and out of fights amazing passive ability Nimble Fighter, with the potential to reduce minion damage to 0

CONS: squishy early on vulnerable to CC limited against ranged champions hard to master the multi-targeting (will be explained in full further on)

30-0-0 mastery spread. However, with his abilities, you can get away with it rather easily. As you can see, all the points are in those that boost AP, AS, and crit. But why AP with AS, and not AD? Again, we go back to Seastone Trident. While the initial attack damage is based solely off of his AD, the effects of all auto attacks are where his true power lies, with the DOT, which scales off of AP and damage currently on the target. As such, AD is not only not necessary, it is rather useless with Fizz

Again, I know I am going to get greifed, but as you can see, the runes are entirely for AS. Again, it is to help boost the potential of Seastone Trident. Another option is to change out the Glyphs for AP or Magic Pen, both of which would add additional damage per hit on Seastone Trident, as well as boost your other abilities as well. However, the numbers are so slight and the abilities do not scale well (other than Chum the Waters), they do not provide a very noticeable difference late game.

First and foremost, most people should understand when to purchase consumables (potions, elixirs, etc), not to mention the necessity will change game to game, so I will not presume to tell you when to buy them. However, the rest of the purchases will not change too much. Also, note I do not tell you when to buy some of the sub-items. Some of them, such as Sheen (for Lich Bane) should be bought early, but the exact time is up to you, as you see fit, though I would recommend right after your shoes. Also, keep track of your gold throughout, and try to get as many kills as possible, and never forget the gold you can get out of the jungle, as this is an extremely expensive build (just over 17K gold)

Hextech Revolver is a great, and under-rated, early game item (it costs only 1200 gold, you should be able to buy the whole thing after your first recall). It is build from the most basic AP item ( Amplifying Tome, which is your starting item), two of them in fact, and therefore provides a great early game AP boost, not to mention its passive, which provides a bit of early game survivability through spell vamp. It also builds into a great multipurpose item, Hextech Gunblade that provides AP, spell vamp, life steal, and a nice little active that slows and damages opponents.

The boots, Sorcerer's Shoes, should be fairly obvious. Boots are always a must early game, and magic pen is helpful for Fizz. Another option would be the Berserker's Greaves, due to the increased attack speed, for the same reasons as the runes and masteries.

Guinsoo's Rageblade is not as obvious of an item choice, however, take a closer look at it, and you will see it is exceptional, and that you cannot beat the stats for the price. It provides additional AP on two fronts, with a flat 45, plus an additional 6 that stacks every time you use an ability or attack, up to 8 stacks. That is an extra 48 AP at full stacks, for a total of 93 AP. The best of any item, other than Rabadon's and Zhonya's Hourglass. In addition, it provides 35 AD (not all that much, but it helps). The key though, is the extra 4% stacking AS, that stacks along with the extra AP. Keep the stacks at 8 and you can decimate.

Also, for you who say "Well, Fizz is a Burster, he should not build up stacks!" Here's a little hint: Farm, get 8 stacks, then W->Q->auto-attack a few times->E->E->R. Now, tell me how that isn't dealing great bursts?

Rod of Ages is a great AP/survivability item. It provides 450 heath, which will make it take longer for the enemies to kill you, and provides both 525 mana, and 60 AP, which allow you to do more damage for longer. The extra health is excelent (though, don't think that it will last all that long...you still have no sort of armor), and lets you attack that few extra times that could be the difference between a kill and a death. However, the true shine comes from the mana. Fizz's abilities can leave him very mana hungry, so that little extra mana allows you to do at least one additional rotation of your abilities. But, all that said, still leaves out the important part. The passive. Every minute after you buy the item, the stats increase. You get an extra 18 health, 20 mana, and 2 AP. It does not sound like a lot, but after 10 minutes (the limit of the stack....), that is an extra 180 health, 200 mana, and 20 AP. That gives you a total of 330 health, 725 mana, and 80 AP. All of which are very high by themselves. Combined, that is a lot of "whoop-***" for only 3035 gold.

Rabadon's Deathcap. What else needs saying? The penultamate of AP, this baby provides a flat 140 AP (massive), along with a passive of increasing your current AP by an additional 30%!!! That means, just for buying this, you get 182 AP. That alone is a massive amount for one slot! Add in everything else, you get 513.5 AP total with all items, at minimum levels. Add in the extra stacks from Guinsoo's Rageblade and Rod of Ages, and you get an additional 88.4, for just over 600 AP. That is not a number to be trifle with.

The last item is really situational, however, Lich Bane is a good choice overall. It provides 80 AP, which is great (when combined with Rabadon's, which you should have all ready, that increases to 104 AP), it also grants you 7% increase in movement speed, 300 mana, and 30 MR, all of which enhance your "assassin" capabilities. The movement speed helps you get in and out of fights quickly, the mana allows you to use you abilites more, and the MR helps you take just that much more damage and survive. The shining point here, however, is the passive. Each time you use an ability, your next basic attack deals an aditional amount of damage equal to 100% of your AP. In this case, an extra 600+ damage. Add that to your AD of about 200, you are dealing 800 damage with a basic auto attack, every 2 seconds. Assuming all of your abilities are on cooldown, that is an extra 2400 damage in 8 seconds, on top of your abilities and auto attack. That will take down even the most health stacked, armor stacked champion.

Seastone Trident is the most potent ability and can get you kills, even after you die. It's passive boosts all of your basic auto attacks by 30-70 (+.35/AP) +4-8% of the targets missing health as magic damage over 3 seconds, which means that it gets much stronger the weaker your opponent is. For example, lets say you have it at level 5, with the ~600 AP of all the items, and you are attacking a target with 4000 life. The first strike will do ~200 AD, and 70+210+16 or 296 damage over the next 3 seconds. If the target is all ready down to half health, or 2000, that increases to ~200 AD up front and 70+210+176, or 456 magic damage over the next 3 seconds. As you can see, it can really stack up.

That is not all there is to Seastone Trident, however. When you activate it, not only do you still get the passive benefits, but for the next 5 seconds, your auto attacks deal an additional 10-50 (+.35/AP) damage up front. You also will apply a grievous wound to the target, reducing any healing they receive. This is like a short-cooldown Ignite, that works off of a melee-range (or about the same range as Ignite if you use it in conjunction with Urchin Strike.)

Urchin Strike is a great initiator move, that has a short cooldown at the higher levels, while not costing a lot more in the way of mana per level. It does 10 / 40 / 70 / 100 / 130 +.7AP+your current bonus from Seastone Trident. With them both at level 5 and all of your items, that is ~200+420+50+210=880 straight off of the top, apply a grevious wound, and deal an extra 70+210+70=350 over the next three seconds, for a grand total of approx 1230 damage. From one attack. Brutal.

Playful / Trickster is a great all around mobility move. It can be used to engage and deal damage, prevent you from being targeted for just under a second, or even slow your enemies. When you first activate it, you become untargetable for .75 seconds, and jump in the direction of your mouse onto your trident. You then can choose to just drop in place, or leap even further. Either way, you deal 70(+50 for each additional level)+.75AP in an area around where you land. The difference is if you just drop, you affect a larger area, and you slow the surrounding area by 40(+5 for each additional level)% for 2 seconds.

Chum the Waters is a very potent harassing/initiating move. It is a skill shot/trap that sticks to the first champion that it hits, or stays on the ground where it lands and attaches to the first champion that walks over it. Then, 1.5 seconds after you throw it, a shark jumps out of the ground wherever it is at, dealing 200 / 325 / 450 +100% of your AP as magic damage, knocks up whoever it is stuck on, and knocks back anyone around them, slowing everyone by 50/60/70% for 1.5 seconds. In addition, when it sticks to someone, it slows them by the same amount. If you get a direct hit, that is 3 seconds of up to 70% slow, plus a knock up, and ~1050 damage with all items. Therefore, it can be used as an additional escape move to slow your enemy down while you run away, initiate a fight, chase an opponent who is trying to get away, or get a kill.

Your passive Nimble Fighter is a build in Ghost without the speed boost. You ignore all unit collisions, and you also take reduced damage that increases with level.

As you level, start off with Seastone Trident, then Urchin Strike, then Playful / Trickster for your first three levels, then Chum the Waters> Seastone Trident> Urchin Strike> Playful / Trickster, with the only exception being grab a second point in Playful / Trickster at level 10 to help lower the cooldown.

Seastone Trident has a nice on-hit effect that applies a damage-over-time debuff on your target. But it has one major drawback. IT DOES NOT STACK!!! Each hit after the first only resets the 3-second time on the debuff.

So? What is the solution? Multi-Targeting.

It is a rather simple idea, but it is very difficult to get it down right. To get the most out of the debuff, you want to apply it to as many targets at a time as you can (usually around 3-4, depending on your overall AS.) So how does it work? Simply in between each auto-attack, you need to click on a different target! So, when you are surrounded by minions, and you start attacking, click on one, and as soon as the attack animation starts, click on the next one, and so on. That way, you continue to keep the debuff active on several targets, thus maximizing your damage output.

Now, that said, against champions, that all goes out the window. You obviously want to focus just one to try to take them out while not taking a lot of damage.

I saw a video that explains it fairly well, when I find it again I will add it here.

As we all know, the Stat Chart at the top of a build does not take into account stacks and add ups from items, so, to help out, here is a new stats chart, with maxxed stacks on everything:

Health 2428
Health Per 5 Sec 21
Mana 2195
Mana Per 5 Sec 14
Armor 68
Magic Resist 82.5
Attack Damage 180
Crit Chance 0%
Crit Damage 0%
Attack Range 175
Movement Speed 406
Ability Power 641
Attack Speed 52 % (if I did the math the right way, please correct me if I am wrong...)
Life Steal 15%
Armor Penetration 0
Magic Penetration 20
Cooldown Reduction 0.0%
Dodge 0.0%
Gold Per 10 Sec 0
Reduced Death Time 0%

This section is based off of input from others, and as of yet has not been tested. The second build highlights the changes.

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Runes

These runes sacrifice large amounts of AS, for a more well-rounded stat build, providing Armor, MPen, MR, and a nice boost to gold income (important, as this is an expensive build, costing just over 14K gold)

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Masteries

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Items
As you can see, there are a few changes to the items, focusing more on your AP, while still providing some AS. However, you loose a little bit of AD, health, and most importantly, lots of mana. As long as you remain frugal with your abilities, that is not an issue, however, it can be limiting. On the flip side, it does provide additional mana/5 sec, as well as a fairly large CDR, which, when combined with all ready low cooldowns, allows you to maximize your burst.

Thanks to jhoijhoi's Guide for making a Guide for tips on layout and design.