Leveling Rapid Fire early on is unadvisable, since Tristana's low base Attack Damage early on the game doesn't make much use of the AS steroid. Wait until you buy some AD items such as B. F. Sword.
Rapid Fire is applied to the next autoattack's wait period - cast it right after an autoattack to squeeze as much as you can from the duration.
If you know you will get an assist or a kill on a champion that is running away then you may use Rocket Jump to make sure your team gets the kill and this allows Tristana to either Rocket Jump out of a deadly situation after Tristana has got a kill or jump again to set up another kill.
Using Rocket Jump to leap over an enemy and then using Buster Shot to send them flying back to your allies or an allied turret can be very effective, but be careful about using the strategy in large team fights.
Remember that Rocket Jump resets on kills or assists; this makes Tristana a very potent turret diver mid/late game. Jump into tower range, finish off the fleeing enemy, and then jump away again to escape.
Be careful when using Rocket Jump as it is considered a "dash", even though it is visually a "jump". This means that if you jump over a trap (like Yordle Snap Trap) you will activate the trap and its effects.
Use Explosive Shot on enemy champions who rely on regeneration or healing. This severely drops their chances of survival, as it reduces their regeneration/healing by half.
The passive of Explosive Shot is surprisingly useful in farming - if there are a lot of minions in a relatively confined area, killing one could burst the remaining minions and gain a lot of gold in a relatively short time, without the use of abilities.
Building an Ionic Spark early on, can help you develop faster, since it combo's quite nicely with Explosive Shot. Once you get to middle game, getting in front of your own minion wave, and mass slaughtering can give a VERY decent flow of gold. Once you get you're 4th or 5th core item (and have the gold to spare) sell off Spark and finish the build off in style!
Tristana's low base movement makes it difficult for her to chase enemies or to escape. This is especially prominent at low levels. Getting Boots of Speed quickly is highly beneficial. Be sure to watch the enemy builds and pick the proper boot upgrade.
Phage is a very good item on Tristana as she can continually slow and attack enemies due to her long range, giving her excellent chasing and laning ability.
Upgrading to Frozen Mallet later can boost your damage output, allow for more consistent kiting and chasing abilities, and improve your survivability.
Tristana is an AD-carry with massive base damage on 3 of her spells giving her a very powerful early game. However when built AD she does not have scaling for her burst abilities due to the lack of ability power, meaning her mid-game is a little weak. Abuse this, since Tristana late game is one of the closest to unstoppable in the entire league due to massive range, AS-boost and the peeling power of Rocket Jump and her ultimate. DO NOT underestimate her though, as even with a "weak" mid-game, she can and does have decent burst when done right, and any DECENT Tristana player will be working to compensate for this.
Tristana has a huge range when she reaches level 18 because of her Draw a Bead; avoid getting kited.
Early game, her range is fairly short; use it to your advantage to harass her and deny her farm.
Tristana has a lot of burst damage from her abilities early-on - buying early magic resistance along with having a way to escape her/peel her from you can hinder her from zoning or killing you at early game. A target surviving her abilities being cast on them leaves her vulnerable to counter-attacks if they have the health or sustain to stick around.
Standing near the brush can allow you to duck into it after she uses Rocket Jump on you, avoiding a good follow-up from the rest of her abilities. As Rocket Jump is the lynch-pin to her combo, she can then be attacked from range after escaping her without fear of reprisal while it is on cooldown.
Tristana has no long-range poke abilities - having a champion that can do this can damage her freely.
As the range of Rocket Jump is very long, however, being a champion that can escape or having a partner that can peel that is likely also a requirement.
Tristana is vulnerable to being hit by skillshots during the animation of Rocket Jump (being essentially a very slow dash) and hard crowd control can stop the ability entirely while it is casting, returning her to where she started.
Move away from a low health minion at early game to avoid the damage from her Explosive Shot.
Tristana mainly deals damage from her auto-attacks. A Thornmail will counter her damage.