Being lvl11 and having bought no champs yet other than Tristana (thanks Malak), I've been trying to figure out how to play her effectively. I've come to conclude that the item build makes her. Early game, people that seem to know what they are doing aggressively push me back from the minions (preventing my explode and increased shot speed), which hurts my $ and leveling. Late game, Frozen Mallet + Bloodrazers = a pretty decent champ. I can't turn the tide of the battle without a good team, but I contribute my part. As long as I wait for a tank to initiate, and not up against someone like Vlad, Trist seems to be working out well. Starting to get annoyed by players that late game start to essentially suicide as if they can kill 3 enemy champs by themselves.
Tristana needs a solo lane to start off well and against only another solo opponent.
Item build I do, along with many others is this.
First two items are Doran Blade and Health Potion (er Candy Corn right now).
Second item is Doran Blade
Third item is Boots. Boots are converted into Zerker or Merc treads. I personally go with zerker for her because she is squishy and the merc treads add about 0.001 seconds of survivability to her on average. Rather just kill me targets faster.
Sometimes I go for a third Doran, as well as others, or I start building madreds bloodrazer. Some go to infinity edge as fast as possible. Personally I prefer the madreds as I feel it kills faster except against squishies in the early to mid game. Late game the madreds always kills faster.
As for ability order I do this...
W, E, E, Q, E, R, Q, E, Q, E, R, Q, Q, then W and the last R out. Here is why.
Her W is her rocket jump which is basically a magic damage ability. Unless you plan on building an AP tristana, this ability only does OK damage early, and not much at all late game. I use it for escaping and chasing. I almost never initiate with it against a full life hero as it will most likely get you killed. It is best to stay at max range to initiate and pepper your target first. This is why she has the longest auto attack in the game. With Q activated, she can reach insane attack speeds early on for a few seconds. With madreds you can bring down just about anyone FAST.
By getting E up first, you can really wipe out minions waves fast and early on for great pushing. With the doran blades early on for an additional 240 to 360 health, you will be able to hold a lane very well against harassment.
After madreds I like grabbing zeal for more attack speed as well as crit strike and movement. If I have 3 doran blades with boots, zeal, and madreds then I sell off one of the blades to buy a vamp scepter. I then complete the scepter into a blood thirster. From here I can either complete the phantom dancer or tri-force from the zeal. I then can sell off another doran blade for infinity edge or heck even another blood thirster.
If the other team has a Jax I grab a Sword of the Divine. If they have a lot of casters and all their team does mostly magic damage with all having mana bars, then I grab a wit's end. If I'm getting CC'd a lot I grab a veil or quicksilver sash.
On a 5v5 map I typically go with teleport and cleanse for summoner spells. On a 3v3 map I may go with exhaust or ignite instead of teleport. The map is just too small to need teleport for 3v3 and as such it is easier for people to early on get to safety on a tower. Which means an ignite or exhaust to get the kill before that happens helps more.