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 before an autoattack to squeeze as much as you can from the duration.
Since that Rocket Jump resets on kills or assists you may use it to secure a kill, and allows Tristana to either Rocket Jump out of a deadly situation after she has gotten a kill or jump again to set up another.
The cost of Rocket Jump is high compared to her mana pool. Pay attention that you have enough mana before jumping in.
Tristana can use abilities while in the air from Rocket Jump. This allows a very strong, fast combo if you play her as an AP caster.
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.
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.
Combine this with Rapid Fire and she can easily farm up and clear minion waves with an ease. Be careful though, this will push the lane hard which leaves her open to ganks.
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.
While Phage may seem to be a good item to buy due to the on-hit effect that grants movement speed to Tristana; the main item that it builds into, Trinity Force, is not a cost effective item since most of Tristana's damage comes from basic attacks and lacks any low cooldown abilities to constantly proc the Sheen's passive. In addition, the stats that Trinity Force grants to Tristana is very mediocre at best. Because of this, if Tristana needs movement speed, it's better to build flat attack speed items that grants movement speed such as Phantom Dancer, Statikk Shiv, and Zephyr instead.
Be careful when picking Tristana, as an enemy's blind can render you fairly useless. A Quicksilver Sash can be used to counter blinding champions such as Teemo and to escape other hard CC's.
Due to her high AP ratios on her abilities, Tristana can also be built AP if your team requires an AP nuker as well as an AP support due to being ranged with decent crowd control capabilities.
Similar to the original AP Master Yi, Tristana loses her DPS potential with a full-AP build, but gains newfound burst damage to whittle down targets and in teamfights, she can potentially one-shot them. However, this type of build offers very risky gameplay, as Tristana must make sure to play safe due to lack of strong-auto attacks, as well as her general squishiness.
Lich Bane is also great item for her AP build, as you can get in extra proc from your Rapid Fire.
Morellonomicon is another great early game item for Tristana as it offers Grievous Wounds to all of her AP ratio abilities and not just for her Explosive Shot, and the cooldown reduction and mana regeneration also helps.
Like with Lich Bane, Nashor's Tooth in combo with it can not only provide cooldown reduction and attack speed for Tristana to retain DPS, but due to the procs scaling off her AP, it can make up for her lost ADC style.
The Howling Abyss
The Crystal Scar
The Twisted Treeline!
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 defenses along with having a way to escape her/peel her from you can hinder her from zoning or killing you at the 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. Randuin's Omen and Frozen Heart are good options to counter build against her, since it will greatly reduce her damage per second output. A Thornmail will counter her damage, but generally is a less better option since it helps to defend only yourself.
Try to not engage her when she can easily escape with her Rocket Jump and Buster Shot off cooldown. The exception is when you can hold her in place with Crowd Control long enough to kill her.
If Tristana is building AP, be very cautious and ward well as she may jump out of nowhere and one-shot you easily. Also, missing calls can prevent a lot of her potential ganks.
In team fights, do not leave any squishy teammates in the front and prepare some CC for her all-in. Be sure to back away if your team have multiple low health allies. She may get multiple kills because the cooldown of Rocket Jump resets whenever she gets a kill or assist.