Corki is a bottom lane AD carry. His style is very different compared to most adcs. He is a bursty, caster styled adc with a very strong mid-game. Since his ultimate has a cooldown of 2 seconds, Trinity force is his main item, as its active can be used many times in fights. Corki has a long range escape/engage with his W: Valkyrie. He also has strong long range poke and armor shred in teamfights. Corki provides 3 types of damage, physical, magic, and true (goodluck building against him).

Pros
-Great escape/engage
-fast wave clear
-long-range poke
-high burst
-3 types of damage(magic,physical,true)
-armor shred

Cons
-weak early game
-relies on abilities landing
-slower attack speed
-Can be mana hungry

Corki's farming is easy early game. you get 7 to 8 more true damage on creeps due to your passive: Hextech Shrapnel Shells (last hitting is super easy). Try not to use your Q: Phosphorus Bomb to farm early game, it will burn through your mana quickly. Once you hit level 6, you can start to farm with your ulti: Missile Barrage. you can use it to farm from afar, or to proc your Sheen. an easy way to clear the back three caster minions, is to Phosphorus Bomb them, then shoot your Missile Barrage at the group of casters. You can also lower each minions health to about half, then Phosphorus Bomb them, and you will clear a whole wave at once.

You MUST max your Phosphorus Bomb first. The amount of damage it does is unreal. You will win most trades with other adc's if you can land your Phosphorus Bomb on them after your first auto attack. This ability is also a powerful AOE ability in teamfights. Max E: Gatling Gun second. It provides AOE armor shred in teamfights. This armor shred is applied to the enemy's stats (unlike Last Whisper where the aromor penetration only applies to you). Thus, shredding multiple targets in fights will give large advantage you your team.

Corki's team fighting abilities are one of the strongest compared to any adc. Corki has many AOE's that can hit multiple targets at once. His Gatling Gun provides armor shred on enemies and it is essential to turn it on when a fight begins. Landing your Phosphorus Bomb and activating Trinity Force with your Missile Barrage, is the highest priority for you in fights. If you time your ulti incorrectly with Trinity's cooldown, your damage output will be greatly reduced. (remember that your passive: Hextech Shrapnel Shells works with Trinity's active)

-Always keep track of your mana bar. You should never commit to a fight if you don't have mana remaining for your W escape(50 mana)

-Try to lead your Phosphorus Bomb behind the other adc when in lane. Most adcs will walk straight backwards after an auto attack trade.

-Remember that your 3rd Missile Barrage will shoot further and will do more damage than the others. Try to always land it.

-Use your Valkyrie to help position yourself in fights, but be careful of nearby CC and gap closers.

-Get Sorcerer's Shoes early, since most of your damage early and mid game is magic damage. You can sell them later for Berserker's Greaves once you have your main AD damage items (optional).

-Don't be afraid to poke your enemies down with your Missile Barrage. It only costs 20 mana. Be sure that you have at least 2 or 3 leftover before you engage into a teamfight.

-Learn to time your abilities with Trinity Force's cooldown.