iAlpha, here with a guide to hopefully help you learn more about League of Legends. I'm currently Platinum, on a shiny road towards Diamond.

As of the current meta, Tristana is considered one the strongest AD Carries in the game. If not, the best AD Carry in the game. She is able to trade damage significantly well in lane and out scale anyone later in the game with her overpowered range and attack speed steroid "Q".
This link to the tier list can be very helpful, giving you an idea of where different champions place. This tier list indicates the stronger champions of solo queue.
http://www.nerfplz.com/2014/08/2014-champion-tier-list-solo-queue_30.html

Tristana definitely has dominance in the game and is the top of the tier list for ADCs, playing the strongest ADC does not mean she doesn't have weaknesses.

PROS
- Able to trade damage in lane very well
- Outscales any other ADC
- Longest range in game (Late Game)
- Strong engage and disengage with her "W" and "R". (Getting a kill or assist resets her "W")

CONS
- Very dependent on support during laning phase.
- Long cooldowns for "W" meaning less space for mistakes.
- Weak Mid-Game
- If behind in CS and KILLS, it is very hard to come back from this hole. This goes for all ADCs in general but it is significantly harder for Tristana.

Farming is very vital to any role, but is significantly important to ADC. An average you should be aiming for is 70 farm by 10 minutes, or 90-100 by 15 minutes.

Creep score is important, however it does not mean that you should take unnecessary damage no matter how tempting it is to kill that low minion. Play smart.

At the beginning of the laning phase, it is important as Tristana to hit level two first. Try to shove the wave, but take into consideration the last hit on minions to gain gold in addition. This enables you to have the level advantage giving you the first opportunity to poke. The poke combo should be "E" first, then "Q" and get in an auto or two. In this situation, the wave is also pushed, meaning they must either try and trade with you or lose minions.

In the midst of the team fight it is important to position yourself behind the team and attack the champion that is closest. Attacking the closest champ whilst staying towards the back means you won't get carried away into the middle of the fight.

Remember, you have considerable long range mid game and the longest range late game. Use this to your advantage.

Only use your jump aggresively when you are assured to win and not die (3v1) or when you are chasing/picking off the enemy with your team. Tristana's ability to jump after a kill or an assist is very advantageous in a situation of whether you want to kill or get out.

Stutter stepping is a fundamental that all ADCs should learn. Stutter stepping is moving towards your desired destination whilst dealing damage in intervals.
(Move, auto attack, move, auto attack, move auto attack and so on)

Fighting in a stationary position only makes the kill on you faster. It is dangerous for a ranged champ to be fighting melee range.

https://www.youtube.com/watch?v=dgMMxTofZ5A
This is a very helpful guide made by the well known CiderHelm. Check this out to see a more in-depth guide on stutter stepping.