I highly suggest getting E first and maxing it by level 9 because it is your strongest in lane/poking ability and does the most damage out of all of your abilities. I then max W because although it may by good to engage or escape with, it's even better when used as a high damage dealer early, mid, and late game. Your Q will be received at level 13 due to the extreme need of CDR and Damage addition to your other abilities. I Do not get Q until I MUST because AP Tristana has no need for any attack speed in lane nor does she do enough damage with her basic attacks to justify putting points in her Q early game.

Note: If you are against getting Q as late as possible then I would suggest an early Tri force, Nashor's tooth, or Hextech Gunblade.

I use Magic Pen Marks to get more early penetration with my E and W when poking in lane. It's common for most mid laners to have MR in their early build and runes/masteries. I use MR Glyphs to avoid taking too much early damage against AP mid laners. Note: This is somewhat of a gamble because there are multiple AD mids that can compete very well with AP Trist. Last off I use Flat AP Seals and Flat AP Quints to increase my early game damage.

If you want more early damage output and/or you are more aggressive I've tried all out flat AP marks and seals as well and it works very well but only when played against champions that are less bursty then you or have early sustain items instead of flat damage. A summoner that using defensive runes and masteries as well as offensive items will most likely beat you if you are using flat damage and no defense or penetration.

Farming with AP trist can get a little tricky. Her E passive Explodes enemies that have been destroyed by her basic attacks. At first sight this seems as if it is an advantage in wave clearing which it is but only if used right. In most cases, this passive causes most new AP trist users to lose farm instead of gaining farm. Remember when farming with trist you need to basic attack all minions instead of just one in order to get them all about 1/4 Health so you can shoot one more basic attack and they will all blow up.

In order to play AP trist against a normal AP mid who isn't as skilled as you, you may not have to use certain unique skills and strategies. Sometimes there will be AD casters or especially strong counters to AP trist that usually win lane every time (For example Zed or Veigar). Early game most mids will seem much stronger than you in an "all out" first blood fight.

Here are some tactics that I use to win lane against harder lanes.

Smart poking: Not only does Tristana's E passive work on minions it works on champions as well. As I farm in a lane I love using my E to poke champions but when champions like Ryze start Catalyst I need the extra poke damage. I try to curve the lane by stay on one side of it and while they attempt to farm I continue to kill the minions around them, forcing them to take even more pokes then their catalyst can out sustain. The combonation of Tristana's E and E passive forces people out of lane and is common to cause an early First blood due to the early aggression for farm and kills of your opponent.

Bounce Engage Technique: This technique is basically the combo I use when I think I'm ready to "all out" a opponent in lane. This technique can be used in two different ways depending on where you and your opponent are fighting in the lane. Here's how you do it: Use E, W onto the backside of your opponent but at the same time place yourself close enough for your W to do damage to them, Ignite them, and use your R to knock them back. This technique does so much burst damage and damage over time that it is nearly impossible to live through if your items are well built up at this point. I noticed the earlier you do this the more likely you are to kill your opponent. Try doing this when you have a level advantage because it could be the difference between killing your opponent or not. My favorite time to do it is when I hit level 6 and my opponent does not yet have their level 6 ability. The other way of using this combo is when you are losing lane and farming at tower and you force them back to the turret using the same combo which causes them to take extra turret damage. This also works well when being dived by more than one opponent because they take more damage in such a short amount of time then they can use to kill you at your tower. This can be the difference between getting two kills at tower and living or dying and getting no kills.

Bounce Engage/Disengage Technique: This technique is to be used when getting ganked in the middle of your combo. Some games I'm willing to gamble the fact that I do so much damage that I can take on multiple people and get out alive while still receiving a kill on my main laning opponent. Here's how you do it: As you E and W to your opponent and the jungler shows up in the lane use your ignite and R on the mid laner and run away from the jungler as you wait for the opposing mid laner to die from your DOTS (Damage over time effects). Once your first enemy dies use your W's Kill Reset to then jump away or Re-engage on the jungler. That is the best way you can engage and disengage during a gank. The only time I use my reset to re-engage is when im very fed, the jungler is underleveled, or the jungler is already low enough from jungling for me to kill them.

Using your resets to your advantage can be the cause/difference of winning or losing a team fight. Although Tristana is a great engage champ in a 1v1 lane, when I come to team fighting engaging at the wrong time can get you and your team killed. A big rule of mine with AP trist is to never be the first on my team to engage. With Tristana's W she simply has no disengage unless she receives a reset which will be to difficult to achieve 1v5. Just as other AP casters, Tristana will be one of the main focuses for the other team in team fights, especially when fed. When a team fight is initiated by my team or the opposing team I like to stay in the back and wait for the perfect time to jump in on either the opposing mid laner or the opposing ADC so you can receive your first reset. From this point continue using your abilities and resets to take out their stronger player and eventually their tank and support.

Pros

Amazing Mid/Late game damage
Good Escape/engage technique
Good farmer with her E passive
Great poking in lane with her E
Very good at securing kills with her W and E

Cons

Very Squishy to AD casters
High Cooldowns
Not good at going "All in"
Early Game damage isn't the best
Easily shut down once Fed.
When not Fed very weak.