Tristana is a phenomenally fast ranged shooter and can be easily the best dps ranged champion in the game if built correctly. It's not crazy to think that she can have her attack speed at the max of 2.5 at times, I've done it before and it's amazing. However, you must know how to use her and utilize her abilities correctly.

Because she is ranged, she is good early on to injure other champions from a distance and force them to recall more quickly than a melee champion. However, her damage isn't much early on and never really gets too impressive until later on. Early in the game she needs to watch out for ganking as she has low health and not much armor at all. But, when you get the Bloodthirster and you have good attack speed, you will have no problems taking any opponent 1v1. With this build it is simple to kill the dragon (3v3) quickly and with enough lifesteal to heal on it. She's killer for coming behind on ganks as her range gives her more shots if the opponent runs.

Tristana, with this build doesn't start of very good (being a carry type, this makes sense). Focus all of your energy on getting minion kills. To successfully make this build, you MUST get many many minion kills. Be sure not to go too deep or you will die as Tristana doesn't have much for health. Focus on getting all the minion kills you can get. It's good to go solo if you can to help get more minion kills (using turret camping or whatever).

Early in the game spam rapid fire, using it as your first skill you get. At level two, you NEED to get explosive shot. This allows you to (passively) damage all opponents surrounding a minion that you kill. It also can be used actively to hinder enemy healing, good for chasing people down.

When you have purchased the boots, the game begins to get difficult as you get your phantom dancer.

Use ghost/exhaust defensively.

This part of the game is most difficult. You have to continue to collect gold on minions and play very defensively. Save up for the phantom dancer and as you work your way up the tree for it, you will noticeably get better. This will help you to get more and more minion kills.

When you get your ultimate at level six be sure to use this wisely. It is NOT effective to push enemies with it for the hell of it. Rather, wait for level 7, get your rocket jump, launch over enemies and buster shot the back to your team. Be careful not to do this in big standoffs though, it's best for 1v2 or 2v2 settings.

Use ghost defensively, and exhaust to help your teammates finish opponents.

At this point you should have your phantom dancer and black cleaver. They're damn good right? Well continue to dominate minions. You are beginning to be able to hold off or push other champions solo. Your explosive shot should be helping you get significantly more minion kills as it can now often finish minions via it's passive ability.

During this time, you need to be utilizing the rapid fire ability that we leveled up all the way. While active, your attack speed should be near or over 2.

When you've gotten the bloodthirster, and are working on the infinity edge, it is a good time to kill the dragon. Because of your attack speed/damage, it's very possible to heal off of it, so don't fret going in solo. When you get that 280 gold (3v3) go ahead and keep working on infinity edge.

Use ghost and exhaust offensively.

When you get infinity edge, the game is basically over for the other team. You are no doubt dominating minions, but the only thing holding you from being entirely unstoppable is your attack speed. After infinity edge, sell your doran's blade and get a second phantom dancer. You will then be unbeatable. If the enemies are pushing, be sure not to die and refocus your attacks. You will be able to kill nearly anything.

Use ghost and exhaust if you even have time before you kill them (:

Doran's blade and the boots are recommended and great starter items.

Phantom dancer is 3rd and it's the hardest to save up for. Just keep spamming your rapid fire and finish off minions and slowly work for it.

When working on the black cleaver, get the attack damage item first, the attack speed second. This gives you more power right away and then additional speed.

After the black cleaver, you should have no problems getting money. Actually, the rest of your team will now that you're killing all the minions (: Get lifesteal first with the bloodthirster, then more damage and you are a walking rapidfiring healing monster!

If you have enough time to get infinity edge, you will undoubtedly destroy the other team, this is late in the game and tough to get to. Keep up the minion kills!

If you still haven't destroyed the other team, sell doran's blade and get a second phantom dancer, you will then be unbeatable.

Tristana's ult is incredible. She can either save the life of one or more allies, or bring death to one or more opponents. Her ultimate, Buster Shot, does loads of damage, pushes, and temporarily stuns enemies.

Ganking:
For ganks, Tristana should be behind the team, allowing the other players to push a little bit (preferably into a turret) so that they get themselves into position. When they are in position, come out of the grass and use Buster Shot to push enemies into your allies paths. The enemy will likely run away as soon as possible, to ward against this in case of teleport, ghost, or anything else, use Rocket Jump to finish them off. One of the great things about Rocket Shot is that it resets the cooldown every time you get a kill OR an assist. This allows you to finish off an enemy even if there are other champions around, you can just Rocket Jump in, then Rocket Jump out over a wall or whatever.

Defense:
Tristana has low armor and life, so, inevitably you will find yourself running from champions or a gank at some point. To get away, use Rocket Jump if you can (over a wall is the best and fastest technique). However, if there is no wall or Rocket Jump is unavailable, you need alternate ideas. If you are being chased by two champions who are close together, you can use Buster Shot to push them and stun them shortly while you make your escape. It is best used if they are directly behind you and close together as Buster Shot can push more than one champion given they are in close proximity.

Finishing:
If an opponent runs from tristana and it looks like they may get away, the best thing to do is Rocket Jump in as close as possible and use Buster Shot to finish them off. This only works if they don't have a ton of health left, otherwise it will just help them run away.