Start: Long Sword
Not because it's a great starting item (it isn't), but it isn't terrible and it's an ingredient for our first face-raping item.

Wriggle's Lantern
Nice for minions and can help you take jungle early or help your team take down dragon much faster.

Zerk Greaves
Nice attack speed.

Infinity Edge
Easily the most dramatic 1-item DPS increase in this build.

SITUATIONAL (Buy all if needed! In order)
Wit's End
If there are 3+ mana users or an annoying caster carry like Veigar, this can work wonders. +40% attack speed, 42 mana burn(damage), and some helpful MR. Savagely underused item.

Madred's Bloodrazor
For tanky teams or annoying health-based tank carries like Cho'gath and Vlad.

The Black Cleaver
If you end up against Garen, Rammus, Amumu, or other armor stackers. Much better than Last Whisper after the recent patch.
END SITUATIONAL

Zeal into Phantom Dancer

The game will usually be decided by this point.

Black Cleaver

Finish with Bloodthirster

Early Game
Play defensively. Don't just start blasting away at the creep waves: you want last hits. Wait for a minion to be a one-shot for you and take it. Then hang back until the next one. If your opponents creep wave progresses, just tower hug and keep trying to last-hit. Having the creep wave closer to your tower decreases the chance of you being ganked, and allows for epic Tristana combos:

The "WTFPWN"
Once you get Buster Shot, when your opponent closes in on your tower and starts chipping away, you can make them pay dearly. Rocket Jump just behind them, and, while in the air, hit them with BS. It will launch as soon as you land and blast them into your tower. They are now slowed from RJ and right next to your tower. Exhaust, hit Q and laugh as the tower (hopefully) starts blasting them. Make sure to hit them with your DoT as they run past you to safety. GG. This happens quickly and is nearly impossible to counter when done correctly.

Mid-game
You should have taken mid-tower by this point. If it is safe to do so, go to a lane and initiate a gank. Tristana is great for this. Hide in the bushes and RJ in so that you can immediately Buster Shot an enemy into your allies and/or tower. Hit Q again and laugh as you reel in the kills. Use Teleport to 1. Recall quickly, buy, and Teleport back without missing a single minion 2. Defend towers and/or initiate ganks. During team fights Tristana is going to be (for a smart team) the first focus priority. Rocket Jump away accordingly and let your team beat them down while they chase you. Once they give up, go back and help your team. If you can keep them from deciding who to focus on, you will win.

Late-game
Tristana is ridiculous. Take out every tower and get every jungle buff. Destroy a mass of minions in seconds. Take quarters of health (for squishies) with every auto-attack. Don't go out on your own and stay alive as much as possible. FOR THE LOVE OF GOD DO NOT INITIATE. Let your teammates go in to the fight first. Tristana CAN GANK, but you must be absolutely sure that your target will have ZERO support from their teammates, make sure you make note of any Shen, Panth, TF, Shaco, etc.

The only ones that are critical are flat health Quints and armor pen. They help massively early game as they allow you to harass aggressively.

If you would like to see this build in action, add me in-game (Aeromir), and I will gladly play a match with you. My K/D ratio is usually between 2/1 and 5/1.