What you want to do is max your Rocket Jump first because this works both as an escape ability and an offensive initiation. Since it can slow, you can stop enemies from enemies to getting away. During the beginning of the game, your damage output is very low, even with a doran's blade. So the way you want to do damage is to use your abilities.

After getting your doran's blade and boots(and potions if your not doing very well), you want to build an Infinity Edge because it will give you good damage output and it is very good for poking because when your playing Tristana, your going to be trying to zone your opponent, and criting is very helpful for doing that.

Summoner spells are entirely your choice but I suggest that you always get flash or ghost because those are great escape abilities, but then its also good to get offensive abilities, ignite or exhaust are good. I use Exhaust and flash because you can use them both offensively and defensively.

Pros:

Tristana, in late game, can deal out massive damage

Tristana's ult is helpful for getting away or helping an ally

Tristana's E is a great farming tool, so make sure to level it fast

Cons:

Early game, Tristana is very squishy so be cautios when first blood is still up for grabs

Make sure to stay at the back of a team fight, like all ranged carries, because you want to minimize the damage dealt to you. As well, go for the squishiest or the highest damage doing enemies to make the fight easier.

If you are doing poorly, then you should get a banshees veil in order to increase your health and mana pool. Also, a frozen mallet could increase your durability but still give you better damage output, not to mention how helpful the slow would be.