So Tristana has probably been my favourite dps champion as I'm a tank player and Trist is super easy to get the hang of after a few games. Which led me to write a guide to her, perhaps its not the best playstyle ever but its a playstyle that you will have success with aslong as you play smart.
By playing smart I mean not giving yourself away to easy ganks and making sure that you are last hitting minions not auto attacking them. If you can follow my guide while getting your items at a decent rate you should be come an absolute beast in the later areas of the game as Tristana has the most insane damage output and tower pounding abilities.
Summoners / Runes / Masteries
Flash and Cleanse, basically with Tristanas rocket jump ability and flash + cleanse she becomes ridiculously hard to kill as she can put a huge amount of distance between you and your opponents. You could trade the cleanse for ghost or ignite if you really want to but defensive summoners on a carry are a lot better than aggressive summoners.
For the runes I have armor pen quints and marks which are standard on any range carry, if you want to use hp quints go ahead
Mana regen per level seals, basically just to keep your mana up, pretty simple logic there
Magic resist per level glyphs, now this you can feel free to change to more mana regen, cooldowns or now magic resist glyphs.
21/0/9 - basically a normal set up for any ranged dps character, as Tristana is mainly an auto attacking champion I don't really see the need for ability cooldowns.
You want to start with a dorans blade, it gives you hp, attack damage and some life steal but if you wish to use a dorans shield thats fine aswell.
Next buy your normal boots, I wouldn't worry about upgrading them just yet, you have a built in escape so you can just jump away and over things to get away.
Next you want to start building your core item which is the infinity edge (the big yellow shiny sword) it hits hard and because Tristana has built in attack speed you can put out some serious hurt with this. You want to buy the pickaxe first up (if you can afford the BF sword buy that first but you will find you probably won't be able to) then just proceed to build the rest of the items.
Now we can upgrade our boots (if you did before you finished the IE thats fine I do it aswell sometimes), I generally go for the berserker greaves but if you want to go for merc treads thats fine but the greaves will help you put out more damage output.
Next you want to build the last whisper, basically with the Ie and LW Tristana will destroy anyone and hit through them like cake, it gives you some attack damage and 40% armor pen which is just so much (gg tanks).
After you have those two items it doesn't really matter what you want to build, I'd generally build a banshees veil just for extra protection but if your team is destroying them you could grab a phantom dancer, black clever or a blood thrister.
With Tristana you want a solo lane, usually mid but top works as well, as you are going to be your teams main damage out put you need the most creeps and gold its all logical.
Don't auto attack the minions, wait till they are nearly dead and then hit them, this may take some practice and I recommend going into a custom game by yourself and sitting in mid clearing waves until you can perfect this. While doing this you should always be moving around, never stop clicking, it makes you more evasive to skill shots and can put you in good positions to harass your opponent.
As you level up on Tristana your range will increase via your passive, so you will be able to stand back further out of the enemy champions range while farming which is actually really handy. Make sure you are constantly checking your minimap (every 5 seconds) to see if you should be pushing up your lane or staying back in case you are about to get ganked.
You are a very squishy champion like all range carries, if you get yourself out of position in a team fight you are going to die very quickly, you want to be putting out damage and not getting hit. If you are new to the game you will struggle with this as your just beginning, its hard to learn how to position yourself but it will come with practice (practice makes perfect), sit at the back behind your tanks and just try hit whoever you can as a you attacking somebody is better than a dead you.
Tips and Tricks
Your W is an amazing escape ability, jump over walls, jump away (combine with ghost to make sure you get away).
Your utli combined with W is a nice little thing Trist has going for her, jump over your enemy (behind him) use your utli on him and he will get knocked backways, preferably into a turret or your team mate. This takes a bit of practice you have find yourself jumping into their turrets range as believe me I've done it and paid for it so try not to do that.
In a teamfight, save your ulti, if one of the enemies champions just manage to get through your tanks then you can just blast him away again and probably kill him before he can get back to you.
I haven't played Tristana in awhile, when I do decide to play her again I'll get some pictures up of how I have built her and my scores.
Feel free to check out my other guides were are on the right side of the page