Not Updated For Current Season
Corki's the first guide I've written for this site. I love him, think he's versatile, and far from overpowered, so your brain won't disintegrate when playing him like it does when you play Mundo or Tryn. He's what they call a pusher, which means if you have a decent team and get near a turret, no diving is necessary, as you can keep the enemy team pushed back solely with your ultimate, which they cant afford to take hits from for long and will entrench your team safely within turret melee range and out of the enemy team's effective range. He makes turrets happen.
Don't mess this up. You have the full level gatling gun early (level 9 I think) so use it on the mob waves when not bushwhacking (keeping the minion waves midlane by merely last hitting to prevent an inferior laner from letting the turret do all his work). If you can bushwhack and starve the enemy (push him back with gatling gun charges, then Valkyrie out), do that, but beware this opens you up to ganks from the river. Alternatively, use the gatling gun to push the minion waves quickly into the turret and nab a few hits on the turret each time around. Focus on last hitting in either case and peg the enemy laner when possible and smart to do so, as Corki has relatively high damage early-mid game (see his passive).
I don't pay attention to the exact levels at which you get skills ( I know your ult is available at 6, thats about it) but the order of priority is this: Ultimate>Gatling Gun>Valkyrie>Phos Bomb. Unless you're playing against a stealth type team, in which case you MAY want to level phos bomb over valkyrie, which is primarily an evasive dash. Basically you're Yi with range and 10% damage built into true damage in your passive. Think like you do when you play Yi. When you charge, charge. Commit. See the below farming guide on how to best lane with him (in my opinion one of the best laners in game). Your Gatling gun will always do the equivalent of 2 auto attacks over a few seconds, and add some armor debuff. DO NOT UNDERESTIMATE THIS DAMAGE. When Corkis auto attacks get out of control, after a kill or 2, this can make people run for the hills (the animation is pretty overwhelming) while you rip at their backs.
Some will preach Frozen Mallet, but I wont. If you hit them from the correct direction on the map and use your Valkyrie wisely (when you know you have enough time between killing the guy and the cooldown to not need it to evade counterattack) and hit your ultimate bombs with any kind of accuracy, you just wont need it. Don't be afraid to pop your ghost to secure an insecure kill. When your face is being ripped off in team fights youll be glad you have the lifesteal (which is somewhere near 50% with the Executioner's Calling and fully stacked Bloodthirster). When focused in team fights as Corki, valkyrie into the background, auto attack (with vengeance) a few minions, and youre ready to charge again. Starting with boots makes you a better harasser and less susceptible to first blood focusing, and allows you to remain in the lane longer with 3 HP potions (very likely more than a starting vamp scepter would give you anyway). From then on it's basic AD carry, Inf. Edge, Black Cleaver, you can throw your own brand into the mix with stuff like Sword of the Occult if you want, but the tried and true AD carry items are what I threw into this guide. Some people will actually go Attack Speed with Corki, saying it gives him better maneuverability with the Phantom Dancer, but Gatling Gun doesnt applies procs (the AS build would call for Madreds) and you're as fast and evasive as you need to be with Valkyrie. I can see Corki maybe getting the Sword of the Divine (Activates to nullify dodge) against Jax, but even thats a stretch. Go AD. When you get 1k crits and can Gat Gun for 2k more in the time it takes to sneeze you'll thank me :)
I run ignite ghost on this type of guy, maybe teleport ghost depending on how incompetent I think my team will be in holding up their towers. The ignite is kind of superfluous to Corki in a lot of cases, as if you're any kind of good with the long range bomb ultimate, finishing people off shouldnt be an issue. I also put the executioner's calling into this build to show the variety of options you have for shutting down enemy healing (especially Mundo's). Pop that ghost if you know he's got a chance of outrunning you before you can fully unload. Get the kill, forget the cooldown.
Go AD. Level Gatling Gun. Don't miss your ultimates, remembering that it's splash damage, and that hitting a minion near the guy is just as good as hitting the champion. Be aggressive knowing that Valkyrie can get you out of a jam, and that in about 70% of cases people will run from Gatling Gun, despite what they can do to you in return. Do your very best to be in team fights and strafe during them with your ultimate. Pop in some auto attacks in the "stand off" phase before a 5v5 goes down if you can safely do it. By end game, if you havent fed youll be 5 shotting people in your gatling gun wave. With the true damage passive, not even tanks are safe from Corki. He's up to snuff.