Hello Summoners!
I'm RobiWizzard a fellow summoner and I'm going to post awesome builds.
I tried this build in ranked games and its working pretty well.
So here I come. This is my Corki guide.
Actually this is my first guide:P

We need the damage and the resistances.
That's all i can say:D

Why we put out magic penetration?
Because Corki's Q,W and Ultimate deals magic damage. This magic penetration has a big effect in teamfights. Others not needed to explain.

Blue is cool that's why Corki is blue too.
BT for sustain+damage Furor and Iceborn for kiting, Muramana and Last Whisper for damage and Warmog's for survivability. Buy Manamune for faster stacking

E max is cool more damage ofc.
Q max for second more burst.
Ultimate when u can put a point.

Summoner Spells
Barrier/CLEANSE and Flash. Others doesn't seem to work
Corki's Spells
Q gives vision. After your manamune you can spam it like a boss in lane
W good escape and chase ability, but use it wisely because it has a large cooldown
E simply op. Damage + armour reduction
R OP teamfights. U shouldn't enter in the teamfight until u have 2 missiles left. after that nuke one of the carries. In teamfight just snipe down the enemies with your missiles.

Pros
Burst
Flashlike ability
good farming(passive)
He can keep distance in fights

Cons
Squishy
Needs to get close for bursting
Bad kiting

Good luck Summoner with this build and have fun ;)