Hi, I'm a gold 3 Tristana main with a 75% win rate over 30+ games in ranked and climbing :o I have a lot more Trist games though - just started back to ranked. I will do my best to help.
Tristana does best against low mobility ADCs I've found, especially if she has an engage heavy team. She can get into the fight and do tons of AOE damage if you put her E on a tank. Many of the times, you can do a lot of damage by surprising the enemy with where your bombs are.
Fyi, you give really good leashes with your bomb(I've never stolen a camp XD). In LANING, you want to grab your e first. You can either use this to push the wave at level 1 or to get some harass on your enemies. All depends on who your support is. You can really get those level 1/2 kills on her because she does so much damage with her E if she can proc it even 3 times. Level 2, you wanna take w. You can get kills/flashes with it cause it scares enemy adcs a lot if your support lands CC and you just jump on them and start building up your E. Does so much damage. Then, you get your Q, which just helps you build your E faster. In some lanes, where I know that they have no kill pressure on me, I will take Q second. I do this if I think I can get free hits on their tower or if I can get a lot of poke/a kill on their bot lane.
In mid game, you really want to focus on taking towers. As Trist, you're REALLY good at pushing out waves. If you play smart and are not dying, you will NEVER lose your tower. Your E passive is so good at killing minions fast. So when you push them in, make sure that you put your bomb on the tower, even if you can only get 1 or 2 hits on it. When it pops, it will deal damage to both the ADC and Support, the minions surrounding them, and it will do good damage to the tower.
If at any time, you kill the enemy bot lane (like level 6 or 7) depending on how low you are, you should definitely take drag. Tristana is so strong for taking dragons/barons and you should take advantage of this to secure early objectives. If you take bottom tower, you should start to pressure your enemy mid laner, and if they don't respond fast enough, you should easily be able to get a tower in mid, adding to the gold influx. Usually after taking mid, I'll continue to pressure bot lane if there's a minion wave pushing back to me. Most of the time in gold, the enemy bot lane will still be trying to get that tower. LOL
For maxing abilities, I max E first. Q second. W third. And builds. Now these can vary sometimes in order. I like getting Infinity Edge first cause it gives you really good stats for taking towers/doing damage in general. Statik Shiv can be nice for the burst, but it's really not my favorite item. I'll always prefer Phantom Dancer over it. Somewhere in between that, always get your berserkers greaves. Now next part depends on how far ahead you are. If you're super farmed and fed and they haven't had much of a chance to build armor OR they are a team of squishies, you want to just pick up a Bloodthirster. If it's a team of tanks with a lot of armor, go ahead and get your LW. If you have engage heavy champs, BOTRK is also an option for the 4th item. If you pick up the BT first, always go the LW after. Your last item can really depend on the enemies. Most of the time, if the game is going that late, you want a defensive item. So options are like: GA( my personal favorite) or like Banshees.
Generally, same rules apply with Trist as do with any other ADC. Keep your farm up and position where you can do damage without dying. Not that difficult to do with trist. You can get resets on W and constantly reposition if you are winning fights. Main rule: Just. Keep. Autoing. Kite away and do damage with your E. If you get engaged on, you have self peel with your R. Also, pushing enemies into towers with your R is just fun. LOL
Um, I think that's it. If I missed anything or you have questions, feel free to ask. 