Tristana works best as an agressive snowballer in a killlane. Her early all-in is nearly unmatched, but she needs an agressive support like leona to really make it count.
Most common mistake for tristanas is that they max E, play passively and then usually drop quite a bit duering midgame, another mistake is rushing zeal.
If you don't have an all-in support or a premate that you trust enough for agressive plays, that is certainly a save solution, but it will always leave you with a lackluster midgame.
If you max W however, you get great all-in potential. W gets 50damage per rank, and it resets on fully proccing E, so you can use it twice in an all-in(so it gets 100damage/rank for all-ins), while it also gives alot mobillity and a really powerfull slow. Try to let the opponent push a bit, then jump on them, use E mid air and activate Q for the all in. Once you pop the E and et the W reset, you need to make a decision, either you jump back out and abort the all-in if you think it's not going to well, or you hold it back till your opponent blows his escapes and you need it to chase, or till you really need the extra damage to win the all-in.
All-ins are ofcurse always a bit risky and need some confidence, but there are few that can actually match her. And if you face a strong early laner like lucian or draven, you can wait till 6. Tris ult has a quite big basedamage, and the cc it offers shouldn't be underestimated, as well as the fact that it ads another stack on your E, allowing you to get the W reset faster.
If ahead, tris can then bully most lanes as anyone pushing out of tower can just get all-ined again, she has alot tools to avoid ganks, and if she pushes up to the tower she can kill it quite fast and her E deals solid damage to nearby opponents.
Also, once you're sure you win lane, you can switch from maxing W to maxing E. W max is just for the laneing all-ins, E gives more pushing power and teamfight aoe, Q gives more dps later on and also more tower damage.
For items, don't rush zeal, go straight for BF and pick up berserker's on the way for some AS. Her E has a great ad.-scaleing, and she already has alot as from Q, she doesn't need as from items that much, and with bersekers, her AS is high enough to stack up E rather reliably already.
I like going essencereaver if i snowball as the cdr and manareturn allows for more agressive pushing with E. If i can't get a snowball, i rush IE to get teamfight damage as fast as possible.
After that i usually get a zeal item(most of the time i go runaan's for teamfighting power and waveclear, though PD for better dueling and kiteing can be usefull aswell) followed by eihter IE or ER, which ever i didn't buy first.
Her lategame damage comes mostly from AAs, so you want the crit. However, you already have alot AS from Q, so ad is better than as on her, thus i prefer IE+ER over double zeal.
Another option, especially in setups that have little peel for you, is getting a frozen mallet and staying at 50% crit. You loose some damage, but that slow on your longranged AAs(even on aoe with hurricane) is really powerfull.
Also, always remember that you can use E and R duering your W (not sure about Q, i use it befor W to make sure it's on), so if you find an oppsing squish running around alone, you can just jump at him and unload your shit befor he knows what happens, and depending on level(for AA range) and AS, you can shoot up to two AAs while they are knocked back from your ult. With some critluck, you can kill an opposing adc befor the CC of your ult wears off with close to fullgear.