Introduction
Tristanais one of the scariest champions to deal with late game. She is also incredibly strong in the early game; specifically at level 2 and 6. However she hits a mid game weak point, where she doesn't have enough items to scale with her 90% steroids, and not enough AP to scale with her nukes.
Runes
My Tristana runepage is designed for early game dominance, very much like masteries.
Flat ARP Marks - Best in Slot
Flat Armor Seals - BiS
Flat MR Glyphs - BiS
Flat AD Quints - Can be changed with Flat HP or Flat ARP. I've personally had the best success with Flat AD.
Pros / Cons
PROS
-High range on late game
-Easy escape with Rocket-Jump
-Strong ulti(can escape from massive enemies)
-high attack speed
-good combo with Explosive-shot and
Ignite
CONS
-low mana pool[can also use ulitily masteries for more mana+mana regen)
-Long Rocket-jump cooldown(needs immediatly kill or assist} if it on cooldown n' they chase you
-Can push the lane on early game and make the enemy jungler gank you easier
-Mana hungry when spamming skillsRather squishy
Summoner Spells
- Ignite over Exhaust, without a doubt. Tristana is all about levels 1-6 and 18, you want to take advantage of these levels. What do you want to do levels 1-6? You want to be able to kill, since she nukes really hard during those levels, having Ignite on-top generally insures kills. Exhaust however does scale better into late game, however Tristana at 18 has such long range, rarely will you ever exhaust a target worth exhausting.
- I take heal to be an absolute monster in the laning phase. This allows Tristana to jump in agressively anytime during the laning phase and win exchanges easily. The drawback is that you don't have a Flash to rely on late-game, but instead become much more early-game snowbally.
Skills

Explanation:
You can buy attack speed, attack damage, crit %... but you can't buy range.
712 At level 18. Second only to Kog'Maw with W on.
Attack Range scales incredibly well with items, making this passive one of the best late-game scaling passives in the game.

Explanation:
The strongest AS steroids in the game. This and her passive really defines Tristana as an AD carry, as they scale so incredibly well with items. The mana cost is incredibly high, so I choose not to level it at 4.

Explanation:
A very clumsy escape, but an escape/initiate ability none the less. The animation for Rocket jump is less than perfect if you compare it to Flash, however it's still a very strong ability. Rocket Jump should be used with caution, especially in team fights, however, Rocket jump should be used very agressively in the laning phase, also very agressively in winning fights, where you can clean up entire teams in a flashy manner by constantly refreshing the cooldown...

Explanation:
I level Explosive Shots at level 1 not because I enjoy pushing my lane, but for the 110 magic damage, along with an early level 2. Ensuring that you and your support is level 2 before theirs is a huge advantage, especially if your support is something like Alistar. If played correctly you can immediately zone or score a kill when your enemies are not suspecting it.
The healing debuff is nice, especially in AD vs AD duels where both have life steal and certain champions (Vlad, Soraka, WW, Mundo... etc). The animation, however, for Explosive Shot is also kind of clumsy, and most of the times I recommend auto attacks over using the ability.

Explanation:
Once Trist hits level 6, she becomes incredibly strong with Buster Shot and has a lot of killing potential.
The damage from Buster shot becomes non-existent late game, and the ultimate becomes primarily used for the knockback.
Looking at recent AD Carries like Vayne/Caitlyn who has pure AD Scaling, this ability is pretty out-dated in terms of design, and I'm not sure why Riot hasn't changed it to AD scaling.
Early game
Try and convince your team into an aggressive support like Sona or Alistar. Then be very agressive with your early level 2 from Explosive shot. Farm to the best of your ability, it's tricky with Explosive shot, but a strong Tristana player can last hit near perfectly
Mid game
Trist's mid-game is horrid. Rocket Jump and Buster Shot's damage become sub-par, Rapid Fire still hasn't scaled up yet.
Even if you've had a successful early game, you cannot get too cocky during Tristana's mid game. Realize how strong you are, and farm to the best of your ability. Try and avoid fights especially if you've had a stagnant early game.
Late game
This is when Tristana becomes a beast, you should be able to solo just about anyone at this point. Your range and damage combined can shred even the tankiest of champions. Don't forget to farm just because you have 4-5 items. Having a QSS before an end game fight may win you the game.
Team fights
Positioning - being able to maximize your damage without dieing.
That is ALL you need to do in fights. It's very hard to teach how to position, but it all comes with your general knowledge of the game; where all champions on the map are, what items do they have, how much hp/mana do they have, what level are they... etc
Final Comments
Tristana's early game is fantastic, make sure to take advantage of this early game, because you will need it when you enter Tristana's mid game. Realize when you're becoming weak and try and avoid fights while farming into your end game build. Once you get to end game, all you need to do is focus on positioning and you should take the game easily.