I've actually been wanting to learn Tristana for a while. She's definitely one of my favorite AD carries, but I'm absolute shit with her and at the ADC role. I actually got a smurf to hopefully learn the AD carry role, but it's still under level 20, so PvP games are a bit chaotic.
I wouldn't recommend smurfing, what i do personally when learning a role/champion, is i play a small number of coop vs ai games, (maybe even some custom games too) then maybe some Twisted Treeline and Dominion, because they are short and let me get a feel for the champion, and then i play some normal games in SR and try to pick that champion/role as often as possible, and i try not to suck too much.
When playing Tristana i usually start with boots and potions, but sometimes i take a doran's blade, and i pick the explosive shot as first skill (then i lvl jump and explosive shot + ulti until lvl 7-8 when i start putting points in rapid fire). Then once in bottom lane, what i do is last hit minions only until i feel like i can push to the tower to chip away some health or destroy it (usually better if the bot bush is warded and at least 1 bot enemy is not there).
During the laning phase, except last hitting, i do a lot of moving back and forth, staying behind minions or sometimes even further away depending on who i'm facing, but i try to always be in range to get xp when a minion dies, and getting the last hit as often as possible, while using explosive shot + autoattack (sometimes even 2x autoattack) to harass.
It's important not to spend all your mana doing that, but if you can keep their hp down, you'll provide more opportunities to get a kill (when your support initiates and then you jump on top and use all your burst dmg it usually works), but also you'll be able to destroy the tower faster because they'll go back to base, and if they have a healer, he'll tend to be low on mana if he has to heal all the time (sometimes he won't even be able to keep up), and then there's the psychological aspect, if they fear you because of all the harass, they'll be less problematic to deal with than if they're confident because you play very safe.
There's often a moment, when trying to get early kills as Tristana, where you want to jump on top of a guy, and you want him to run away because that means he's not attacking you while doing that, and for 2.5 seconds he'll be slowed by the jump AOE, but if he does attack you back, you have to know when it is safe to just stand there and trade blows, and when you have to run away (but then it was probably a mistake to jump in the first place, because jumping back is a lot safer but now it's going to be on cd). To stay alive, it's important to keep ready to use rocket jump instantly when for instance you see a Taric using his stun on you or something like that, but most of the time just moving normally while staying just outside of other people's range and watching the minimap for gankers is enough.
Knowing when to use your ultimate is another important part, i found that i often use it to help someone else escape by pushing back gankers (the push-back effect has a small aoe so it can push a pack of enemies), but sometimes it's also good to use it in reverse, to push someone in your turret, teammates, or simply further down your lane to give them more ground to cover to go back to safety while you attack them, and in rare occasions it can be used to finish people, but you really have to use it only when someone would otherwise escape your range and they have like 2 hp bars left, because in many situations you can push them to safety with low hp (but then again sometimes if they have dots -damage over time- on them, like explosive shot and ignite or red buff, they will die anyway). For summoner spells i tend to use teleport + heal, for map control and safety/sustain and to waste no xp/gold in lane, or sometimes i want to clear a big minion wave or push an undefended tower and teleport is just the right tool for that. Mostly i use those spells because Tristana has alternatives to flash (her jump), exhaust is often too short ranged and you have a slow already in your jump aoe, and ignite can be replaced by explosive shot when you want a dot with anti-healing properties (plus, once again, ignite is often too short ranged to use reliably). The heal can often be used to save a teammate or fill back everyone's hp a little bit during an important push, so it's still good lategame, and it's obviously useful in early.
For items you'll want the usual AD stuff like Berzerker greaves + Infinity's edge, Phantom dancer, Bloodthister, Last whisper if they build armor and a survivability item for lategame like Banshee's veil, Frozen mallet, Guardian angel or even Warmog sometimes. Mostly you'll want to buy the smaller items first like BF sword, Vampiric scepter, Zeal, Pickaxe, etc..
Oh and as you'll see, lategame you can destroy people by just frowning at them, but you're still very vulnerable to burst damage and CC so it's often required to stay behind and play safe during teamfights, unless people are so scared of you they just run away or they lack the burst/cc to beat your raw damage and lifesteal.
That's the basic guideline, anyway, after that it's mostly practice and soon you'll understand how she works (she's really simple actually).