In this guide I am going to run through the basics of Corki and also the basics of an AD Carry, this may be telling you stuff that you know, but I feel that it is better to know too much rather than not enough.
Corki is an AD carry and can deal out an incredible amount of damage, especially with his ultimate and his Gatling Gun which is very scary for a group of carries.
For runes I like to run with the following.
Red Runes: Greater Marks of Desolation.
Yellow Runes: Greater Seals of Might.
Blue Runes: Greater Glyph Of Shielding.
Quintessences: Greater Quintessence of Desolation.
For masteries on Corki I will go for 25/5/0 picking up all of the damage as possible from the Offense masteries. I like to be able to output as much damage as possible and then if I need to I will get some defensive items.
Hextech Shrapnel Shells: This ability is great for bringing down tanky champions, it is one of the best passives for carries in my opinion.
Phosphorus Bomb: This is an excellent ability for stealthy characters along with helping to last hit on a bunch of low minions.
Valkyrie: Another great ability, I believe that the best ad carries will have an extra kind of escape or dash away from the danger for example, Tristana, Graves and Corki.
Gatling Gun: Your scary damage will come from Gatling Gun, it can tear through AD and AP Carries. I tend to try and max this as fast as possible once I have got one point in my other abilities.
Missile Barrage: Corki’s ultimate is a great poke and is great for chasing down enemies, it also does AOE damage which is good for clearing minions aswell. It is not an instant heavy nuke like Graves or Tristana, but it is a great ultimate.
My recommend items for Corki
Last Whisper / Madreds
Those are my recommended items, if you get past them then you can either go for a phantom dancer to add speed and crit or you can go for a guardians angel and a banshees veil.
During the laning phase your main priority is to last hit the minions to get as much gold as possible. If you try to zone out other champions with your support then great, but remember the best time to go for a champion kill is when it is unfair, so I tend to wait for the Jungler or Mid to come down for a gank. Once you get your ultimate it is a good idea to try and poke champions down a little.I will initially go for a Dorans Blade for a good balance of health and damage. After going back once more I will get speed boots and some potions.
Mid Game / End Game
During the mid game once you get your infinity edge your damage will be awesome. You should get this fairly quickly if you have been good with your last hits.In team fights always stay back and let the tank initiate, after the tank has initiated I tend to poke with my ultimate, then Valkyrie in and Gatling gun when the enemy are already focused on another champion.Gatling gun will do a lot of damage so remember to make sure you use it at the correct time.If you are taking a lot of damage then I tend to save heal to bait people in and then Valkyrie out if you need to.
Some general tips for playing Corki would be to not get too greedy. It can become easy to want to jump in with Valkyrie and Gatling Gun, but Corki is a carry and can die very quickly.Try and poke enemies down with your ultimate and phosphorus bomb and then burst with Gatling Gun and your basic attack.