Tristana when she is played well can be the bane of your enemy.

The combination at lvl 6 of

"Rocket Jump" over their heads

"Buster Shot" towards your turret

"Rapid Fire" and "Exhaust" help to keep them in tower range while you deal large amounts of damage quickly

"Explosive Shot" damages them as they try to run away and if you think they may get away then "Ignite will usually finish them off

If you think that you may die, in order to escape

"Exhaust" the enemy chasing you

"Buster Shot" them away

"Rocket Jump" further away from them

unless they are Pantheon or TF you are going to be able to get away the vast majority of the time.

The reason i went for archaic knowledge is because it effects your explosive shot which early game can give you a kill. Also in the late game if you have a heavy mage champion group it means that your team mates will be able to rip them apart.

The reason i didn't put 4 points into alacrity is due to rapid fire. Also the point could be spent in a better mastery

The reason i choose to level explosive shot first is because it is really good for herasing your opponent and if they try to run away can still land you a kill.

I level Rocket jump second because it allows you to easily escape from a gank and it allows you to catch and slow your opponent as they try to run away.

I level rapid fire last because early game it is useless except when combined with the combo i mentioned. Also because of this build you are likely to get quite a few kills which will make you the prime target so leveling rocket jump before rapid fire allows you to escape.

Ignight is a good spell to choose because if explosive shot and rocket jump are on cooldown it may give you the kill.

Exhaust is good because it will provide you with plenty of time to either kill your opponent or bring them extreamly low.

Flash is another good option because it can be used to help you either close the gap on your opponent or to get a greater distance between you and your opponents.

Ghost gives you the same benefits as Flash.

Clarity is good early game because it allows you to stay in lane longer and keep up your herasement but not as useful late game as you are not likely to run out of mana.

Cleanse combined with either flash or ghost makes Tristana incredably difficult to kill as you can run away and break out of all stuns and slows that get placed on you as you run away.

Teleport is good because it allows you to quickly join your team in the enemy base or allows you to quickly jump to a turret to defend it if one of your team has gone back to buy or if they have died.