Here's everything else you need to know. (EXPLANATIONS ARE ON THE LAST SECTION)
LANING PHASE: (EARLY GAME) Corki can harass and remain stationary, so buy boots or Doran's for whichever style. (boots, agressive. Doran's, stationary) Clear the minion waves using your passive for your advantage and your Q. This helps you obtain all the last hits if done well enough. (MID GAME) During teamfights try using your W so that every enemy takes atleast 1 tick of it. Since all of Corki's abilities are AOE, you might as well team up with a Malphite. <

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Might not happen in Ranked. Corki is a mobile champion so you're good to go in and come out if things look bad. (LATE GAME) Since you have reached this point of the game, you might as well focus down their carries (AP and AD), then focus their tank, yes, their tank. Corki's cooldowns are so low that you might as well focus the tank. Let your team focus their top and jungler.
ABILITY INFORMATION: Phosphorus Bomb is Corki's main damage dealing ability, mainly for bursting. It has a low cooldown so spam as much as you want in TF's as long as you don't run out of mana.
Valkyrie is Corki's third damage dealing ability which you will use to manouver around the battlefield while dealing damage to the fools that chase you. Dont spam too much since it has a much longer cd than Phosphorus Bomb.
Gatling Gun is Corki's utility ability (based on the fact that you do have an AD carry) which reduces enemies' armor if hit by it. Try using this as early as possible for maximum damage from your Carry. Also try coordinating this with Lichbane.
Missile Barrage is Corki's ultimate which goes extremely well with Lichbane. You just have to time it right. Great for harassing and taking down enemies that tremble before the might of the AP Corki.
BUILD INFORMATION: Buying order: Boots/Doran's,(boots), Lich Bane, Arch Angel's staff, Rabaddon, Rod of Ages, Tier 2 boots, Rylai's. Build explanation: Lich Bane goes well with Corki's low cd abilities, Arch Angel's because you need mana and mana regen. Rabaddon for maximum ability power, Rod of Ages for tankyness, Rylai's for more tankyness!
EXPLANATION FOR EVERYTHING: AP Corki always surprises your enemies, hate as much as you like, first guide, sorry for all the confusion caused, AP Corki is one of those rare AP carries that deal stable damage instead of burst. Corki can also burst, but not as effectively as most AP Carries. Please do comment and fill me in with some of the stuff I might have missed. I was hasty about all this since it's late and I am going to play some more LoL with AP Corki. Also, criticism is appreciated, helps me improve my guide. Also, don't forget to read the pros/cons chapter! :D

CONS: CC can shut Corki down, Soraka alone can shut Corki down, requires an above average player, requires blue at most of the time.
PROS: Stable and burst damage, exceptional harasser, strong at every period of the game, good mobility, good kit overall, harassive abilities.