Draw a Bead[Passive]

Innate: The range of Tristana's basic attacks, Explosive Charge.png Explosive Charge and Buster Shot.png Buster Shot is increased.
Bonus Range: 0 - 136 (based on level)

Rapid Fire [Q]
Cost: No Cost Cooldown: 20 / 19 / 18 / 17 / 16 seconds
Active: Increases Tristana's Attack Speed for 7 seconds. Attack Speed: 50 / 65 / 80 / 95 / 110%

Rocket Jump[W]

Cost: 60 Mana Cooldown: 22 / 20 / 18 / 16 / 14 seconds Range: 900 Area of Effect: 3500
Active: Tristana launches herself to target location, dealing magic damage and slowing surrounding enemies by 60%.
Kills, Assists, and max Stack Explosive Charge.png Explosive Charge detonations on Champions reset Rocket Jump's cooldown.

Magic Damage: 95 / 145 / 185 / 245 / 295 (+50%)
Slow Duration: 1 / 1.5 / 2 / 2.5 / 3 second(s)

Explosive Charge [E]

Cost: 50 / 55 / 60 / 65 / 70 Mana Cooldown: 16 / 15.5 / 15 / 14.5 / 14 seconds Range: 525
Passive: Enemies explode when slain by Tristana's basic attacks, dealing magic damage to nearby enemies.
Active: Places a bomb on an enemy or turret that explodes after 4 seconds, dealing physical damage. Each attack and ability charges the bomb's damage by 30%.
At 4 charges, the bomb explodes immediately. The detonation radius is twice as large if used on a turret.

Passive Magic Damage: 55 / 80 / 105 / 130 / 155 (+25%)
Active Physical Damage: 70 / 80 / 90 / 100 / 110 (+50 / 75 / 100 / 125 / 150% bonus) (+50%)

Buster Shot [R]
Cost: 100 Mana Cooldown: 120 / 110 / 100 seconds Range: 525
Active: Tristana fires a massive cannonball at an enemy unit. This deals magic damage and knocks surrounding units back. Magic Damage: 300 / 400 / 500 (+100%)
Knockback Distance: 600 / 800 / 1000

Pros
Great early game
Snowballs easily and can carry games quite quickly after that.
Isn't really hurt too badly by not snowballing or even behind due to her good farm.
REALLY mobile.
Her ult prevents people from chasing her down, or a little extra burst damage to grab a kill.

Cons
She tends to fall off a little bit late game, if the enemy team is way ahead or both teams are full builds.
She suffers a lot from hard cc.

I've touched on this before but generally early game you're gonna farm safe hitting as much as harass as you can (E passive works really well for this when you kill minions it does AOE damage, a small amount but every bit helps!). Then when the time is right, you strike, usually after support has used their main cc/damage or when your support lands some good damage/cc. If the latter is the case, make sure you play around the support, you can W in so you have a lot of range to work with.

We go press the attack because this gives allows Tristana to dash out the most DPS, by hitting enemies 3 times in a row, they will take increase in adaptive damage. This has a very good synergy with our explosive charge ability. Allowing us to deal massive damage during the early game and potentially securing first blood.