This build has been pretty reliable in solo queue. I'm not a hardcore player who cares about ELO or ranked stats. It may not be the mathcrafted best possible build, but this guide should definitely help players who are new to Tristana understand various angles on how to play her other than straight DPS.

The underlying ideas behind the build are

Increase damage because she can poke from a great range
Increase lifesteal to stay in lane
Increase attack speed and crit chance together
Increase health to make lifesteal gains more effective and reduce danger from high burst damage
Don't neglect AP because her abilities scale well

The end result is a well-rounded Tristana who can deal solid AD and AP, equally formidable in team fights and as a lane pusher. Many champs are not effective when built to be well-rounded, but this Tristana can crush all but the most coordinated solo queue teams. If you try the build in ranked, please leave a comment about how your experience goes!

Greater Mark of Desolation x9 is always a good choice Tristana; pile on Greater Quintessence of Desolation x3 to further boost armor penetration. Use your seals and glyphs to shore up some early-game defenses with Greater Seal of Armor x9 and Greater Glyph of Magic Resist x9. If you want to be more aggressive in the early game, you could try Greater Seal of Attack Speed x9 and Greater Glyph of Ability Power x9 instead.

I avail myself of a ton of offensive masteries, since both AD and AP masteries are relevant. You may want to build a more common 21/0/9 or 21/9/0 mastery tree, but definitely take enough offensive masteries to get Havoc . I like spending my off points in Perseverence to help last longer in lanes early on, and this is usually the only effort I make to compensate for Tristana's small mana pool and lack of mana regen. Resistance and Hardiness are also fine choices for your off points.

No surprises in choices for summoner spells. Here are some acceptable options:

Ignite: Keep healing champs from being as effective and stack more damage over time.
Teleport: Very useful if you need to transition between side pushing, team fights, and base defense.
Exhaust: Always a useful disable.
Flash: For those times when you can't Rocket Jump out of danger.
Ghost: Good for both retreat and pursuit.

I would recommend taking at least one of Ignite or Exhaust and no more than one of Flash or Ghost or Teleport.

Priority for skills is essentially Buster Shot > Explosive Shot > Rapid Fire > Rocket Jump with two points taken early in Rocket Jump.

Explosive Shot is great for harassing the enemies in your lane. Its active ability is a useful deterrent, and the passive chips away at enemies who stand near their minions (enabling you to prevent enemy melee champs from getting last hits). You shouldn't have any problems picking up last hits -- just watch that you don't get overzealous with the exploding minions and push the lane out too far when the enemy team isn't fully accounted for.

Rocket Jump will mostly be used for escapes until you find yourself in a situation where you need to close distance to pursue enemies. The reset on kill or assist allows you to pursue multiple enemies in sequence or dive in for a kill and immediately jump out. If you are in a mid lane, you can sometimes establish early dominance by jumping onto them, using Explosive Shot and Ignite and getting off as many auto-attacks as possible. Few people are expecting such an early assault; if you don't get a kill, you will force them to heal or recall early. Just make sure you know who you're diving -- some champs have a good early-level response to this brash attack, others don't.

Do not put points into Rapid Fire early! Take your time getting last hits and harassing the enemy champs. Use the bonus attack speed later when you're able to focus a single target -- you shouldn't have to use this skill to clear minion waves because of the passive from Explosive Shot. Every second that you spend not firing while Rapid Fire is active is a waste of precious mana.

Lastly, Buster Shot can be used to deal good burst damage to secure a kill or to push enemies back to save a teammate or yourself. Don't use it early in a fight unless you are able to push the enemy into a solid wall -- this skill will knock people through some walls (e.g. in the jungle) and out of some skills (e.g. Cataclysm). If you're super fancy you can jump over someone near your own turret and shove them under it, but it's a tricky gambit. Once in a while you can use an unexpected push to your advantage, but generally you should use it as your killing blow. Try to put Explosive Shot or Ignite (or a standard attack when you have the red buff) on them before using this skill -- if you push them out of range and they survive the shot, the additional damage should tick down their last remaining health.

The items and their order are carefully chosen for the different phases of the match. The last major items can be varied somewhat, but four items form the core of the build.

Start with Doran's Blade for the health and minor lifesteal, then start building towards your Berserker's Greaves and Bilgewater Cutlass. This gives you a good source of early damage, an item with small burst damage and slow, and lifesteal to keep you in lane for quite a while. Rack up the gold on those last hits, because you're going to need it.

Next, build towards a Hextech Revolver and Zeal. At this point you have added crit chance, move speed, AP, and spell vamp -- as long as your tactics are solid, you shouldn't have any issues holding your own in a lane. If you haven't already done so, force your opponents into a low-health situation (where they have to decide between a risk of death or recalling to heal at the expense of XP) or zone them out of XP as your range increases thanks to Draw a Bead. Upgrade these items to Hextech Revolver and Phantom Dancer as soon as you can.

At this point you have decent damage, but so does the enemy team. Tristana is traditionally a glass cannon: high damage output in exchange for poor survivability. You will have decent lifesteal now, but it won't save you from high burst damage: you need a bigger "battery" to store it in, so build straight for Warmog's Armor. You will rapidly approach the bonus cap as you tear through minions. The benefits of your lifesteal increase and you can take more burst damage to survive mid-game team fights. Nothing feels better than getting out of a team fight with 100 HP, transitioning to a lane, and refueling a ton of health as you push towards a tower. (I will be trying a build that uses Frozen Mallet instead, and probably pairing it with Atma's Impaler later on.)

Your final two items can be used to react more to the enemy team.

If your AD is still crushing people, press the advantage. I like getting an Infinity Edge and a second Phantom Dancer so that I have great move speed (on a champ that usually doesn't) and can melt enemies just with autoattack. Alternately, you can go for AP/AD combo items like Lich Bane and Guinsoo's Rageblade.

If the enemy team has responded to you with armor, try rounding out the build with items like Madred's Bloodrazor, Last Whisper, or Black Cleaver.

Lastly, if you're getting focused and the enemy team deals massive damage despite your boosted health, take some defensive items! Tristana is most valuable as a persistent threat, and you can't play that role if you're dead. Counter magic users with Wit's End, Force of Nature, or Banshee's Veil; counter physical attackers with Thornmail, Atma's Impaler, or Frozen Heart. When picking your defensive items, think about how you can adapt your tactics to make use of their other stats (like increased move speed, enemy slow, damage return, or damage boost).

Early Game -- Mid Lane

Know your enemy. If the champ doesn't have a good early CC and you're not at risk from the enemy jungler, you will have two opportunities to launch a quick assault. As soon as you reach level 2, you can Rocket Jump onto the enemy champ, tag him with Explosive Shot and Ignite, and land a few regular attacks. This will kill squishy mages (Veigar, Annie, Heimerdinger, etc.) or cause them to waste Flash and heal. As you reach level 6, Ignite should be coming up again, so you can attempt the same combo with the addition of Buster Shot -- if you've had any success harassing and zoning, you can initiate just before the enemy gets their ultimate.

If you can't secure an early kill, just focus on harass and last hits. Stay out in the field as much as possible -- you do not want to get behind in XP or gold as Tristana. In solo queue you may not have a jungler, so you can take wraiths and wolves if your lane is pushed out uncomfortably far.

Early Game -- Side Lane

Do not initiate fights. Get farmed and chip away at your enemies. You really can't afford to get behind the XP/gold curve in a side lane.

Mid Game

Unless your team has a better pursuer (maybe Olaf or Vayne), you should take the red buff. With your mobility and lane pushing power, you can destroy unprotected towers and force team fights by chipping away at towers in a stand-off situation. Keep your farm up by being first to address any large enemy minion waves.

In team fights, communicate with your team and pick the high-value targets. Wait a few seconds after the fight starts, then move in and activate Rapid Fire and Explosive Shot to take down the primary target. If the target aren't dead after being initially focused, keep them slowed with red buff, Hextech Gunblade, and Rocket Jump. Remember to use Buster Shot as a finishing move; improperly used, you will accidentally save an enemy (like Janna's ult can do sometimes).

If your team has good vision of the map, you can be aggressive in taking dragon as often as it comes up, saving Rocket Jump just in case the enemy team approaches.

Late Game

If the game has been going in your favor, you are now a terror to behold. Your standard attack will harass for loads of damage, and your move speed will keep you in range (but the enemy team can't respond well thanks to Draw a Bead). Wear down the enemy towers when the opportunity arises, but when the enemy champs respond, immediately back away and take potshots to punish them.

On the defensive, as long as you don't get baited away from your team and into a bad situation, you can keep attackers at bay almost indefinitely using your range and lifesteal and large health pool. Once you've chipped away at the enemies significantly, you may be able to Teleport to a pushed minion wave and knock down a tower in no time flat. Your enemies will have to choose between retreating and going after you (but if you recall after taking the tower, they'll fail) or diving your team's tower in a 5v4 situation (but you've chipped at their health enough to make the prospect of winning less certain for them) -- keep pushing if they don't choose either option!

Pros

Solid damage output
Abilities and auto-attack equally threatening
Mobility and survivability on a champ that usually lacks both
Adaptable to different endgame situations

Cons

Not the absolute highest raw attack damage
Difficult to come back from getting behind in gold/XP (true for most Tristana builds)
Limited escape moves if your team is unable to apply CC to keep you safe (true for Tristana in general)