Thank you for viewing my first guide! Fizz is one of my favorite characters because he can dish out lots of damage if you know how to play him right.
When i first played him I was told to play attack speed, and that didn't go so well. So, i stopped playing him for awhile. Then I played him one day being bored and I tried to play him as ap. I ended up doing pretty well.
And that was when i had the brilliant idea of combining these two areas and thus, the build you are reading is here today!
I'd like to give credit to jhoijhoi for helping me make this guide and giving me all these tips and tricks.

DoT depending on the amount of health missing descent escape great initiate ignores unit collision summons a shark, on land...

SPACE

a bit squishy early game not to good in in team fights if your ult is on cooldown

ATTACK SPEED

I decided on the Greater Glyph of Ability Power and the Greater Mark of Ability Power for the extra oomph to the ap area

I then used the Greater Seal of Attack Speed and the Greater Quintessence of Attack Speed for the boost in attack speed

I use the skill for the basic reason that it's used, to slow people down.

This is a wonderful summoner spell if needed to escape or chase after a champion if you playful/trickster is on cooldown.

Other Options!

If you need to take down an opponent that has run away and you don't think that your Seastone Trident will take them, you can use this spell if your having a bit of trouble.

Great for mobility across the map if you need it.

Another great spell for mobility.

Urchin Strike: Fizz dashes a fixed distance in the direction of the target, dealing his total attack damage as physical damage plus additional magic damage to it. The ability will also apply on-hit effects.
50/55/60/65/75 Mana
Additional Damage: 10/40/70/100/130(+.6 per ap)
This skill comes in handy for ganks. Also, it applies on hit affects, meaning your seastone trident affects your target as well. Dealing damage to all enemies passed through, this can be a very useful skill.

Seastone Trident:(Passive): Fizz's autoattacks rend his target, dealing magic damage over 3 seconds that strengthens if the opponent is low on life. Multiple autoattacks will only refresh the duration. The total damage caps at 300 against minions and monsters. (Active): Fizz's autoattacks are empowered for the next 5 seconds, dealing additional magic damage on-hit and causing Grievous Wounds; 50% healing reduction, to his opponent.
Passive Total Magic Damage: 30 / 40 / 50 / 60 / 70 (+0.35 per ability power) (+4 / 5 / 6 / 7 / 8 % of target's missing health)
Active Magic Damage: 10 / 15 / 20 / 25 / 30 (+0.35 per ability power)
This skill is my absolute favorite. It's a wonderful skill to use for farming. It can also be used for bringing down the champions who have lost a lot of healht due to the fact that it deals more damage when the target has less health.

Playful/Trickster:(Active): Fizz hops onto his trident in a nearby location, becoming untargetable for 0.75 seconds and gaining the ability to use Trickster before the effect ends.
If Fizz does not use it, he will slam the ground below him, dealing magic damage and slowing nearby enemies for 2 seconds.
(Active): Fizz hops off from his trident to a nearby location, dealing magic damage nearby enemies in a smaller area than Playful. Trickster does not apply the slow.
Cost: 90 / 100 / 110 / 120 / 130 mana
Cooldown: 16 / 14 / 12 / 10 / 8 seconds
Slow: 40 / 45 / 50 / 55 / 60%
Magic Damage: 70 / 120 / 170 / 220 / 270 (+0.75 per ability power)
Great for chasing. Hop once, doesn't get them. Hop twice, you got them! Even if you don't catch them with this, if your close enough you can charge at them with your urchin strike.


Chum the Waters:(Active): Fizz throws a fish in a line that will bind itself onto the first enemy champion it hits. If it doesn't hit an enemy champion it will stay on an area, and it will stick to the first enemy champion that walks into the area. The champion that has the fish attached will be slowed by 50%.
Regardless of position, after 1.5 seconds, a Shark will emerge from the earth to eat the fish, dealing magic damage, knocking up the target, knocking back all other enemies within the area from the center and slowing all enemies in the area for 1.5 seconds.
Cooldown: 100 / 85 / 70 seconds
Magic Damage: 200 / 325 / 450 (+1.0 per ability power)
Slow: 50 / 60 / 70%
Great skill due to its large slow and ridiculous amounts of damage if you have a lot a ap stacked up.

Doran's Ring Great early game item. For the amount of stuff it gives you, it's definitely worth the price.
Malady Lowers the targets magic resist, gives ap, and increases your attack speed. It is a considerably good item.