Caitlyn isn't called a Glass Cannon for nothing. She shoots at an extremely long range but at the same time a very squishy champion. When choosing a team of 5v5, Caitlyn should almost always mid because her range can provide a good farming experience and possibly deny the other champion laning against you experience. Caitlyn fights best with a tank or another bruiser that can soak up a bit of damage so she can gun her foes down fast.

Generally, Caitlyn either starts a fight, or ends a fight by coming in late. She can start fights because most opponents will be drawn to attack her when she is alone because of her low hp. However, Caitlyn can use her 90 caliber and trap to buy her some time so her teammates can come in for the gank. She also works well coming to the battle late so she can sneak in and chase enemies or simply add some good support damage (Not to mention her Ultimate can snipe fleeing enemies at low hp).

In the beginning, Caitlyn has the most harassing capabilities because of her range and her Q ability (Piltover Peacemaker). She can get first blood fairly easily either laning top/bottom or soloing because of the range and damage she puts on her enemies.

Mid game is where Caitlyn is not so effective because her damage and hp doesn't go up very fast and her items are quite expensive to build. So the best thing to do is give support by adding damage to team fights and leaving. Additional support can be given to help allies escape is by using the 90 caliber net and her yordle traps. These can slow down her enemies and let her add a few more hits to them. However, these are reliable escape methods and quite mana heavy. I would go for some buffs in the jungle for gold and also farm any lanes without anyone because she can push towers very fast and earn some additional gold for your team. This way you can soak up some experience and gold to buy the items you need.

Late game is where Caitlyn shines again, once you have at least a phantom dancer up, and your infinity edge with other damage items, she can start killing champions quickly. At this point in the game, it is really important to stay alive as your opponents will try to gank you first so its crucial to stay behind a tank or champion with slow/stun so your hits will land. Your Piltover Peacemaker isn't as effective but it can harass enemies while you're on the offensive and enemies are tower-hugging. Her Q can hit tower huggers if you stand right outside the turrents range and if you back out before the shot lands on the enemy. Her yordle traps (w) and 90 caliber net (e) won't have much use but slow the enemy down which can offer a small advantage in team fights.

That is just a general strategy to play Caitlyn and how I feel about her after playing mroe than 200 games with her.

Some may ask "why no armor penetration?". Well I think that attack speed is very important early game so you can stand there and shoot enemies that come close to you and also allows for better farming. Armor penetration would definitely be the better alternative for Mark and Quintessence runes as it lets your ultimate (snipe) and Q (Piltover) pierce armor as well. I like attack speed because it has an even greater effect, because it helps throughout the entire game. Armor pen is not very useful mid to late game unless its a percentage like last whisperer. Also, if you want to get a a last whisperer and have your first zeal/phantom dancer wait, that's alright because your berserker greaves and runes have a decent boost in attack speed.

I find for glyphs to be solid mana rather than mana regen or mana/level. This is because solid mana early game lets you casts more Q and still have a boost near the end.

Seals are pretty much your choice, I would go for attack speed if your Quints and Marks are also attack speed, but if you are going for armour pen, then go for armor or magic resistance.

Here's the exact purchasing order. It may be a little weird, but it makes the purchasing more efficient.

Doran's Blade

Boots of Speed --> Berserker Boots (best if you can afford the whole thing in one trip)

B.F. Sword

Vampire Scepter (do not make Blood Thirster yet) [This is a good item for survivability as it keeps Caitlyn in the action and farming for gold, so she won't have to go back to base for hp every time she takes damage)

Cloak of Agility + Pick Axe --> Infinity Edge (using existing B.F. Sword)

Pickaxe + Long Sword --> Last Whisperer (this Last Whisperer can be omitted and skip right to Phantom Dancer if there aren't many opponents stacking armor)

Zeal + Dagger + Clock of Agility --> Phantom Dancer [Extra attack speed, movement speed and critical strike chance...what more can you ask for?]

(sell Doran's Blade now, but a little earlier/later is fine)

Make Blood Thirster

Zeal + Dagger + Cloak of Agility--> Phantom Dancer

Optional: Frozen Mallet, this is always a good item to build last as it gives HP that is much needed late game. The slow affect also picks off enemies trying to leave a team battle as you can sit back and watch Caitlyn gun down her prey and other teammates to gank. This item is optional if you didn't get Last whisperer

Critical Strike Chance is your friend, and with Infinity Edge, you can do 250% damage when you hit, with the masteries and items, there is a whopping 82% of hitting a critical, doing 690 damage. On top of that, Caitlyn's attack speed is so high you just have to position her correctly and she will gun down anybody in the way.

I'm not going to go into detail. Q or Piltover Peacemaker is obviously the best damage skill and should be your priority. You need the cooldown to be low so leveling it up whenever possible is wise. Your ult should always be priority ONE when leveling up just like most other champs. The next should be your E which is the 90 caliber net, sometimes I find myself having to spam this to get out of ganks and it is essential to get the cooldown to a minimum as you level this ability up. The sneaky yordles is useful but leveling it up early doesn't give much advantage, so just invest one point at level 4 and never touch it unless you have nothing else to level up.

Flash - this is an important one because it lets you flash to fleeing enemies to lock in the kill. This spell can also be used around lvl 9+ to tower dive or flash out of tower, after you have killed a fleeing enemy.

Ignite - this is important to use against healers like Mundo and Warwick so your shots actually do damage to them. This is also useful in the beginning to prevent those skirmishes where your enemy has heal and as they flee, there is no running away from ignite. You may ask "why ignite? its a short range and Caitlyn is long range!". Usually you can't stay away from the enemy for an entire kill and as enemies approach or flee from you, pop ignite to add some extra damage.

Heal - this is also an option as I sometimes find myself having barely enough hp to get away from a gank or ambush, but it is not my first choice.

Teleport - this is a good alternative if you're not feeling like ignite because it lets Caitlyn defend towers or push lanes faster. In the beginning it can be used presumably to stay in the experience after making a trip to the town. This is also useful during most of the game because she can teleport in while a team fight is going on and ambush the enemy.

Pros:
-Very long range basic attack - useful for harassing and last hitting minions
-Has some form of escape mechanism with W and E if used correctly. Some thin walls can be jumped with the 90 caliber net
-The Piltover is useful for harassing and killing fleeing enemies
-The Ultimate is EXTREMELY useful for killing fleeing enemies at long range

Cons:
-Very squishy, needs support to be effective
-Easy target if you are in an easily ambushed location
-Ult can be blocked so in team fights it can be very ineffective with many opponents in the way

Its 21/0/9 for a reason. Caitlyn is all offensive and the Masteries make her damage output more effective.

The little bit of Utility should help you better than Defence.

Caitlyn is undoubtedly one of the best farmers in the game. She can shoot down minions and lat hit for gold like there is no tomorrow. The best part is if you farm smart (and not push to hard) in the beginning, you can even deny your opponent experience while they can tower hug and you can last hit the minions. If timing is correct, range is no problem in hitting the minions and squeezing their gold.

On top of that, Caitlyn can also push towers as her range is basically a little shorter than the tower's so she can be putting in some damage on the tower until the last minion on your side dies and still NOT be hit by it.

Caitlyn works well in both top/bottom and mid lanes. On top of that, she can also take on two enemies in a lane when people want to put pressure on her or simply there is a jungler and you have to "man-up" as Caitlyn and take the lane with two opponents. With some mild tower hugging and smart farming, she can stack higher levels on her lane because she is the only one getting the experience, she can send her laning foes back to base pretty frequently for hp!