AP Tristana is an extremely uncommon build, and is underestimated most of the time. Tristana's skill/ap scaling is one of the best in the game, and it's burst is not to be underestimated. Cause of her humongous burst when she's ap, she can be called an ''Anti-Carry'', cause her burst is always enough to atleast take down the carry.
In team compositions, where the team severly lacks burst, ap tristana can be looked at as a savior.

The gameplay feels extremely satisfying, and you can mostly kill anyone with just a small combo.

Pros:

• EXTREMELY high burst
• Great Laning
• High Fun Factor
• Hard to counter when playing properly
• Great Dueler
• A really long jump range.

Cons

• You're going to get focused A LOT.
• Long cooldowns.
• Relatively low HP
• Gets eaten by Le Blanc
• Low mana

Although it's optional to go for Armor seals, I find that going for magic pen, flat AP glyphs, and flat AP Quintessences, give you an extremely strong start, which is important, as you will have to do well when laning in mid.

Masteries should be centered around as much damage as possible. Which is why getting all the AP-raising masteries from the offense tree is important.
Personally I also like a bit of ''toughness'', which is why I went into the defense tree to get the extra HP masteries from there, cause it raises your survivalbility in the early game.

Your bread and butter combo will be Deathfire Grasp + W + E (While in ''flight'')+ Ignite + R.
Tristana is a extremely dangerous dueler, and if all of his CD's are off, he can kill anyone in a flash.
If your dmg is high enough and the enemies are low, you could also try to use your skills on both of them, E + W + Ignite on one, and deathfire + ulti the other one. But for that you would need to attack champions that don't have too much hp. I just tried to make this point so that everyone would be able to understand that just blindly spamming your skills on a target which is almost dead is just a waste, and makes you useless against anyone you might ran across in the next second.

Try to use your skills wisely in a teamfight.
Sometimes you won't even need to use a deathfire as a starting skill for the combo, that you get down a AD carry with just W + E + Ignite + R, and leaving Deathfire for a tankish carry (Olaf for example), can help the team take him down, while you've already done your part in a teamfight.

It's important to know the limit of your dmg output.

There's a summonerspell, which is extremely important on AP tristana and it's *drums* Ignite! Ignite will give you the burst needed to surprise the laining opponent with the dot dmg, and it can easily get you some kills in the beginning.
Flash can be used to escape, and also as something that raises the reach of your jump.

You can also use teleport, exhaust or ghost instead of flash, but I'd like to stress that ignite will raise your dmg output quite a bit.

The most important thing to get is a Deathfire Grasp! Without it you will lack the dmg output to get down a champion from full hp, and it also works wonders on tanks.

As starting items you could start with any of the following:
Doran's ring
Amplifying Tome + Hp pots (To rush Deathfire, which is the best course of action sometimes.)
Boots + Hp pots.
After you got your Deathfire, it's a good idea to upgrade your boots into sorcerers and go for the cap after that.
After the cap, it's a choice between Rylai's and Void Staff. Though if you're having trouble against CC, going for Banshee before that works wonders.
In a good game, where the enemies can't focus you down too well, Zhoniya's hourglass is great.

Other useful items:
Going for a Lich Bane makes you more of a carry, but it really doesn't help you do the instant kill combo, but in a situation where the enemy can't focus you easily, lich bane is an extremely useful item, if you're missing on the dmg department.

I can already see people whining about ''Y NO WILL OF THE ANCIENTS?!''.. The reason is simple, the cooldowns on your skills are too long to get any effective healing from it. Your position isn't standing around in a teamfight, but quick jump in and jump out action.

In a teamfight, you will usually have to be the one who'll take down the most dangerous target.
You should never try to initate a teamfight, as the first thing you'll meet is a bunch of stuns and death (Should be extremely obvious.), though sneak attacking (Jumping) from behind a obstacle, and taking down the carry, followed up by a jump back over the obstacle. But I have to add that jumping out isn't by far as good as taking down the AD carry in a teamfight, simply cause of the fact that if the AD carry is dead, the whole team will go into defensive and it will be harder to push, though when you help the team win the teamfight you'll be able to push as much as you want.
In an incompetent team, doing some rogue action can be risky, but also rewarding.
If your burst is high enough to kill the AD carry in a second, leaving some kills for the heavy AD carry can help you get more ahead. But I have to say that leaving kills as AP tristana is pretty hard.

Try to use your skills wisely in a teamfight!

Tristana is a great character to surprise with in a ranked match. I'm not exactly sure how useful she is in a high ranked game, but in a lower-mid ranked match, she is a pick that will make the enemies run around confused.
Though I do have to say, AP Tristana's arch-nemesis is Le Blanc. Don't go against her!

Try to harass the enemy mid with E as much as possible. Even a skill exchange is OK, cause your E will dmg him much more then he can dish out at you.
With your ranged attack and E, farming should be relatively easy, if you're used to it, but it's quite easy to push the lane with Tristana.

You can start harassing properly from Level 3, and go in for the kill. Just a W + E + Ignite when the enemy has 50% hp will get him down to 0%.

AP tristana is an extremely fun champion to play, and I have to say that no other champion feels quite like her.
Go give it a try!

Here's a couple of replays.
AP Tristana nr.1
AP Tristana nr.2