Penat, if you read the whole guide is should be some solid advice... but I can restate some of the main points...
Farm as many minions as possible, try to get the last his on every minion in lane, and if one of your towers has minions pushing to it, try to be the one that kills then. This also means to kill as many jungle creeps as possible, both while changing lanes and while in lane (see my guide)
Whenever possible, don't use valkarie or gattling gun while in lane, this is a huge mistake that costs a lot of corki's precious mana that could be used for farming/harassing.
Work hard on your positioning, this one is hard to describe, but try to be right behind a tank when the iniation starts, you are also much better at jungle teamfights than lane teamfights because of the narrow passages and your ability to skillshot through walls. Basically though, you want it to be you, two tanks right in front of you, and then their entire team clumped together in front of that dying to gattling + phosph + missles.
Speaking of which, when you are attacking in a 1v1 or teamfight, you've got a lot of skills so don't forget to use them, you should be able to pop out a missle for ~150-350 (doubled if big) extra damage between auto attacks, and that phophorus will from 350 damage on the whole team while adding a blind.
Other than that, just stay careful, don't cross the river by yourself, watch the minimap and communicate with your team...
If you are still having trouble beyond that, try queueing with larger teams, if you can get 4 other players and build a team around having corki mid as the team's carry, you will be able to dominate very solidly