Corki is very squishy. You want to play it safe until lvl 6 then you can start harassing. The key is as soon as you get engaged activate Gatling Gun, with black cleaver you're going to shred 95+ armor making you do bonus damage to most characters. As soon as you get bloodthirster you can start going out and killing everyone. Once you hit lvl 18 with the above items really the only ability you use is Gatling Gun and your auto-attack, which is in the 2's.

You want to rush black cleaver because unless they an armor unit you will be doing massive amounts of bonus damage from their negative armor. Then you want attack speed so your passive gets a little play. then more attack damage and lifesteal so you can kill and still stay in lane. Then more attack speed, lifesteal, and armor reduction. Last more damage for your auto-attack, passive, and Gatling Gun. At lvl 18 with the above items I've had Tryn pop hi ulti running up to me, then six seconds with your attack speed and lifesteal you can kill not only him but anyone easily. (This is a great build to run in 5v5 because your Gatling Gun does AoE and helps your teammates do bonus damage as well.)