I have seen Tristana be built in many different ways. Some like to build her dps because of her insane range, some like to go ap because of her insane scaling (1 scaling on her e, and 1.5 on her ult), but what works best for me is combining the two. With a few ap items here burst is still enough to take out a single target, and with the ad mixed in she can also help out in team-fights. With This build Tristana is really effective against squishy dps's/ap's (burst them), tanky melees (burst, rocket jump away, finish off), and just about everyone else. In a team-fight if you happen to get focused, all you do is rocket jump backwards, and atack from a safer distance. I have tried out some other Tristana builds, but none worked as well as this one. Note: this build works well either solo-miding, or laning with a friend.

Pros

Amazing Range
Amazing Damage
Amazing Burst
Amazing Sustain
Amazing Kite
Amazing Farm

Cons

****ty Early game

Not much to say here. Start with vampiric scepter for the sustain early game. Then try to get the hextech as soon as you can. The boots are pretty self explanatory. Guinsoo's will help you farm, and help you in team battles. Bloodthirster for damage. Rabadons for more burst in team fights. And then the last item I recommend getting another Rabadon if they have a lot of squishies, and otherwise either a phantom dancer or a bloodthirster.

The skill sequence above is mainly to give you a good burst to get fed mid-game. If there's a lot of team fights you might want to get rapid fire sooner, although I recommend maxing explosive shot first for better/easier farming.

Ignite - Damage, plus having to chase is annoying
Exhaust - Again having to chase is annoying
Teleport - Good map control, get back to lane when you die (however with this build you should not die unless it's a 5 person gank

Not Recommended

Smite - Only if you're trolling
Revive - Only if you're trolling
Clarivoyance - Only if you're trolling
Heal - Only if you're new to Tristana
Clartiy - Only if you're trolling
Garrison - ROFL dominion sucks balls
Ghost - What do you think rocket jump's for?
Flash - Only if your keyboard is missing it's w
Promote - Only if you're trolling
Surge - Only if you like turning big for a few seconds

With Tristana, in between last hits you want to attack the middle caster minion, so that when you kill him, he damages the other two caster minions as well. This will help you build up a decent sized group of your own caster minions, which should eat everything especially early game.

Team fights are one of the most important aspects of a game. With Tristana you will have a few basic goals in a team fight.

1. Hit as many champs as you can with your buster shot. Remember, your ult does over 1,000 damage, the more people you hit with it the better.

2. Stay safe. You are a major damage dealer. It sucks dying in the first few seconds, and then watching your team get owned.

3. Take out their main damagers. This can be done in several ways. the way I find best is rocket jumping behind them, and them buster shoting them into your team. The assist will refresh your rocket jump cool-down, enabling you to jump back to your team. If your team is bad/laggy/"other excuses" you might want to flank in from behind and buster shot the squishies into your team, saving rocket jump for the escape.

4. Get fed. Duh dude you're the carry. Although kill-stealing on purpose will get your team mad at you

When you find yourself in a 1v1 situation in a lane you should fight unless they are really fed or out-level you. You have two options:

1. Burst them. If you can kill them in one burst, then obviously do it.

2. If they are not too squishy, do they following.Start shooting them from a distance, you should out-range them due to your passive. If they run away, let them and just keep harrasing until you can burst them.
If they do not run away: Once they get close enough burst them, making sure that your buster shot hits them into a wall, otherwise they will just escape (if they can deal a lot of damage at close range save rocket jump). Once they get close enough to attack you, rocket jump behind them, taking you out of their range, and cutting of their escape. By this time they should be dead.

After reading through this guide you should have what it takes to go out there and show em. If you liked this guide please rate up, if you know how I could improve it, please tell me. Thanks!