Welcome to the "Tristana, the Elf Shooting DPS Carry" guide/build. This is my very first build so any comment or feedback would be greatly appreciated. In this build, I will be covering as much detail on how to become a better player with Tristana, for players of all skill levels.
If you have any comments on how I could change my build to the better, please comment at the end.

First, I have to say that Tristana is by far one of the easiest champions to master. Although she is very squishy, there are definite ways around this. Building a very solid Tristana in terms of AD, DPS, and Life Steal could be what helps your team win games. After all that's said, Tristana IS a carry, so use her to her advantage.

OFFENSE
Since Tristana is one of the most offensive ranged characters in the game, why not put points in the offense section? Tristana is also most effective when she is stacked with critical strike. Near the end of the game, with a massive amount of critical strike and critical chance, along side with extremely fast Attack Speed and high Attack Damage, Tristana WILL be feared.
Important:

-why not have extra damage?

UTILITIES
Going with the 21/0/9 is what I usually do. In the utilities section, there is nothing better for Tristana than getting more experience. Finding yourself a little bit squishy and returning to base a lot to heal? This might drag you back in levels and cause you to fall behind. If you place some points into Awareness , this allows you to stay in the game.
Important:

-extra experience=level up faster=buffer earlier=more power=win.

Optimal Choices

Exhaust
-Exhaust is a good choice because it slows the enemy down, giving you the time to fire away and deal massive damage, offensively speaking. For defense, it can help slow an enemy champion just enough for you to either run back to your tower, or simply just jump away with Rocket Jump.

Ignite
-This is proven to be a deadly combination when paired with Explosive Shot. Double the DoT is always a good thing when champions are close to dying and you want to finish them off.

Not Recommended

Clarity
-As long as you are careful with your mana use, you will be fine. Don't attack minions with Rocket Jump because it is a waste of mana and also a risky move since you are jumping towards the enemy.
Smite
-Tristana is already one of the best at farming with Draw a Bead, since her range becomes massive and on top of that, Explosive Shot has a great passive for taking out any minions in any lane.
Revive
-You only want to use this if you die a lot. But... you don't want to die a lot, so this is not a good pick.

Pick the summoner spells that seem most fitting for a ranged DPS carry. It's mostly common sense.

Level 1: Always start out with Explosive Shot. Why? This is a perfect harrassment tool early in the game. With the splash damage, it's sure to piss off a lot of people.

Level 2: Rocket Jump allows you to have a very good escape mechanism. Jump over the crowd and into freedom!

Level 3: Back to Explosive Shot. More harrassment and when active, deals a decent amount of DoT.

Level 4: Rapid Fire. Sometimes you might just need a little bit more attack speed to finish off weak foes.

Level 5: Back to Explosive Shot again. This allows even more harrassment due to the significant amount of splash damage. If I am correct, the splash damage would be hitting more than your normal hits at this point in the game.

Level 6: Buster Shot. Please get your ultimate as soon as possible. Level up at 6, 11, 16, or else you're just dumb.

Level 7-10: Add 4 more points into Rapid Fire. Finish off those foes.

Level 11: Buster Shot. What more do I have to say?

Level 12-15: It doesn't even matter what you put points into. At this point, you just want to get rid of your points. On my guide, I just put it alternately because it doesn't matter.

Level 16: Buster Shot. Ultimate....? Yes. But by this point in time, Buster Shot should not be a tool used for killing anymore as it does insignificant damage. It should be only used to either defend or escape.

Level 17-18: Finish off the remainder of your points however you wish.

Ah, yes. Items. I will describe my choices in detail, from early game to late game.

Early Game

I always find myself shy of attack speed early game. Despite what all the other builds say to build attack damage first, I almost always build attack speed first. Why?
First of all,
if you obtain a Dagger compared to a Doran's Blade, you have room for a Health Potion which is needed for a character as squishy as Tristana.
Second,
almost all attack items are more costly than the simple dagger. For example, the B. F. Sword or the Pickaxe. Eventually, you will need these items, but do not get them before the attack speed items as this will benefit you more. The ONLY thing that you need to watch out for while starting out with attack speed is not to try to do anything to fancy like harrass champions to a point where you feel greedy for the kill. Only push when you know that you have a chance of escaping in case of a gank. In the early game, play Tristana as more of a support role rather than a carry, because there is not a whole lot she can accomplish while developing her true potential.
Lastly,
I always want to save my mana for escaping. If I build attack damage items, sure it will be more of a harrassing method towards enemies. If you want to kill them faster and if they are in the range, you'd probably use Rapid Fire to add more DPS to help kill them faster. But what I like to do is play more passively, saving up my mana. If a gank comes, I easily have enough mana to escape with Rocket Jump.

Building attack speed with the dagger is also optimal because it allows you to become one step closer to the Berserker's Greaves.

Your first trip back should be when the other person in your lane leaves too, but be reasonable. If you had an extremely good start and are harrassing them and winning, count off about 5-7 minutes before you go back. If the lane is almost at a stalemate, pick your opportunity and work with your laning partner (or watch yourself if you're solo) in order to push them back a bit, forcing at least one person to leave their lane.

The next item that you should be getting is life steal. Tristana does not have a very good natural health regen rate, so life steal helps. The next item purchase should be the Emblem of Valour. This essentially gives you another 10 health regen per 5 seconds, on top of your original 10, so you should have 20 health/5. This is a decent regen rate for a squishy hero. It also adds a +18% life steal. It costs 800g, but it's not a bad investment. It will let you stay in your lane longer for sure.

You may find yourself lacking the raw killing power that Tristana should have, but it helps balance the champion better in the start.

After building the Emblem of Valour, buy another Dagger. Start building towards your Zeal, which would later on become a Phantom Dancer.

Now you see why I start building with Attack Speed first. The Dagger is one of the most versatile items in the game as it can build towards so many different items such as Black Cleaver, Phantom Dancer, Berserker's Greaves, etc.

A reason why Tristana does not really need to build attack damage is that she is all about last hitting minions. With her Explosive Shot, this does damage to other minions (possibly champions) that are nearby. She does not have to kill champions in order to become fed.

Mid Game

Mid game tends to start when people start ganking each other. The laning method is no longer a way to go. When pushing with Tristana, keep in mind that you do not have a great attack damage yet, so beware of all champions, especially junglers, because they can easily gank you if you are not careful.

Another reason for the early attack speed is that even though Tristana is a carry, she is best played in a more conservative way.
"It's not about who has the most kills, it's about the player who has the least deaths." This quote summarizes the way Tristana should be played. Keeping Tristana alive also keeps her in the game. Keeping her in the game means that more can be done with and for your team.

Keep in mind that once you reach an attack speed of about 1.100 or above, then you should start building attack damage. You might actually reach that point with the Zeal only and not even have buy the Phantom Dancer yet. With just the raw damaged gained from leveling up, you should have around 70-80 AD. Farm some more, and then start building attack damage.

The first attack damage item you want to build towards is the Infinity Edge. What you build first is totally dependent on you. If you are struggling early in the game and are looking for just a cheaper tool that helps you a little more, I would suggest you get the Pickaxe first. This might help save you in a sense because you could purchase maybe one or two more Health Potions and could be the thing that saves you in a life-death situation. If you have the gold because you are doing well in your lane, go for the B. F. Sword. Given the +45 damage from the sword or the +25 damage from the pickaxe, you now have around 100-120 damage. Significant? No. Not yet, at least. Sufficient? For the time being, yes.

Once you have the gold, you should now purchase the Infinity Edge. The amount of damage and the critical strike is great. This is a must-have item.

Late Game

After you build your Infinity Edge, start building towards a Black Cleaver. This item is also essential in your battles because it weakens your enemies' armor by the penetration stack and it gives both a very good amount of AD and AS. With a total of around 160+ AD and a 1.800 AS, you are the perfect killing machine, or rather, becoming the perfect killing machine.

Another item I LOVE to have is the Zeke's Harbinger. This is not only good for yourself, but it is a valuable team item. It gives off one of the most effective auras in the game, especially EVEN more armor reduction to your enemies. Upgraded from the 18% lifesteal to 20%, it's not too significant, but that's not the point. It also gives a great 40% attack speed, 20% for yourself (and another 20% from the aura), while everyone else on your team, in range of course, gets 20%. This is great when you have a Melee DPS on your side like Xin Zhao or Master Yi! The added 30 HP5 is also a great aspect. This WILL make your character more balanced.

Most of the guides I have seen do not have the Zeke's Harbinger, but I believe it is a very valuable asset to your item set. Instead of building two Bloodthirsters, try to build a Zeke's Harbinger first and then ONE Bloodthirster. The point I make is that if you get unlucky and face yourself against a huge gank and end up dying, you will lose the bonuses provide by two Bloodthirsters and it will be a hefty cost. Instead, build only one, but it is still as effective.

When you have complete your whole item set, your character should have around 290 AD (which isn't the best, but is already really really really good [emphasis on the really]), and you should easily have over 2.000 AS. If not, the AS should be just under. This way, mana is no longer a problem as you do not need to activate Rapid Fire nearly as much, leaving you more capable of escaping tight situations.

Other Items

Madred's Bloodrazor
- If there is a tank on their side with heavy HP like Cho'Gath, build one of these instead of a Bloodthirster

Last Whisper
- You don't really need this unless they are EXTREMELY stacked on Armor. For example, if they have an Amumu, Taric, Shen, etc.... then you should build one because the added armor penetration helps take them down.

Banshee's Veil
- Buy it if you really need to, but don't build towards it. It's not something that a Tristana should have unless you're getting completely obliterated.

Frozen Mallet
- It gives a good boost in health, but for a champion that requires lifesteal, it's not optimal to get this. Plus, the 20+ damage is minimal compared to other items such as Black Cleaver. The only thing great about this item is the slow. It could help kill your enemies indefinitely.

Team work is what wins your team the GAME. Yes, I said THE GAME.
I will shortly make some pointers on how to become a better team player with Tristana.

Laning

Tristana is a beast when it comes to laning. Whether you are laning with a teammate or going solo, she is one to be reckoned with. First of all, with her Explosive Shot's passive, she can do more damage to more creeps on every kill. With that being said, Tristana is most effective when she last hits minions. This keeps you aware of your positioning (instead of auto attacking and clicking insanely to get back). All you do is step in, take one shot, kill one minion, splash damage and boom. Gold. Tristana is a character that almost ALWAYS comes out of the game with the most overall damage being dealt.

Solo Laning vs. Co-op Laning

Solo laning gives you the ability to become very strong at a very early level, since the EXP gained from the creeps is not shared with another teammate nearby. Last hitting is still in effect.
Another thing that should be noted is that Tristana is a VERY good harrasser. Her passive allows her range to be HUGE. Take this into notice and use it to your advantage. If you are the better champion in mid, you cause more havoc onto their team. Take a shot at the enemy champion here and there and just see if they are smart enough to fall back before they die, or stay and get killed, feeding you.
Once you reach level 6, put a point into Buster Shot and ask your jungler, or another teammate if you don't have one, to come gank the champ in mid. At this point, you want to play as defensively and as passively as you can. If your tower is in range and shoots the ranged creeps and the enemy champ is still pushing, now is the time for the gank to work. Rocket Jump in towards the enemy champ, Buster Shot him towards your tower, Exhaust the living **** out of him and if he is still not dead after that gank, Explosive Shot and Ignite should finish him/her off.

Co-op laning gives you less experience but it doesn't hurt Tristana in any way. In fact, I believe Tristana is best played when she lanes due to the fact that she is a great harrasser and a great support at the same time. She does not always have to play the role of a carry. If you have a melee DPS in your lane, harrass the enemy as much as you can and then let the melee DPS finish the job. Assists are not as rewarding as kills, but a kill for your team is a death for their team. It means that even though you didn't get the kill, it's still rewarding. Last hitting is most important when laning with another person because both of you are trying to farm. Watch for the low health minions and shoot them. When the chance comes for a kill, use the above tactics to kill off the champions. Do not, I repeat, DO NOT initiate a fight because you WILL get killed.

Ganking
Since Tristana is a very slow champion, she is not the ideal ganker. Instead, be the one who lures enemies. If the enemy sees you at 200 health or lower, they WILL go for you. make sure that you are in the right position and not too far out. Make sure that you have called for aid from the jungle (if you are soloing or laning) or from lanes (if you are laning---- this isn't ideal, but it works). There is not much you can do besides sit and watch the bodies hit the floor. The reason why you have to be bait is because you're very squishy, so it's most likely going to be risky pushing too hard.

Pros

The pros about having a ranged DPS carry like Tristana includes:
- Great DPS
- Great range because of Draw a Bead
- Hard to kill if played properly, which means escaping with good combos such as Buster Shot and Rocket Jump
- Amazing DPS ability due to Rapid Fire, but you probably still won't need it unless you want to cap the attack speed.
- Great asset to your team with the addition of Zeke's Harbinger in your inventory.
- Great against champions 1v1

Cons

- Very squishy early game
- Very slow base movement speed
- Really dependent on items
- Really dependent on teamwork
- Have to be quite fed in order to of too much use

Tristana is an outstanding character if played correctly. This gives Tristana a more balanced item set allowing her to be pretty solid offensively and defensively.

I have personally played Tristana this way for at least a couple months, if not half a year. The only reason why I can't say I'm the best Tristana out there is simply because I do not have a very good laptop/computer to run things 100% smoothly. But still, without a doubt, I have finished very strong with this build.

After endless hours of testing, the build that you have just read has proven itself in battle. Even when I go against enemy Tristanas, I can say that I am better most of the time.

Please, if you readers out there have any questions or concerns, or would simply like to comment, any feedback is appreciated. This is my first guide/build so don't expect me to be perfect.

And as for you trollers, please take your garbage and throw it somewhere else.

Thank you for taking the time to read this guide.
Much appreciated.
Cheers!