Let's say that I put a Rylai's Scepter on Corki. This item adds +80 Ability Power. What would this actually do?

It buffs your spells by a different amount.
The amount is different cause some spells have different ratio 0.6:1 1:1 etc.

So basically it will increase the damage of your spell ability by 80 or less depending on the ability power ratio of the spell.

So the damage of Corki's ultimate would also go up?

Yes.
Better go check some of the guides to see if there is a ability ratio of their spells to know the exact damage buff you would get.

Awesome! Cause I am getting a little bored of just buying the recommended items. I want to try and make my own builds but I just need to make sure i understand what each buff means.

Sorry for another question but where can i find these guides? Would it just be on the Guides & Strategy board?

Well yes, here is a list of ''all" guides http://beta.leagueoflegends.com/boar...ead.php?t=4373
I couldn't find though what is the ratio.

By the way the recommended items is for beginners mainly.
There are very different items and style of play for a champion so you are free to experiment and find the one that suits you.

Yep, I used to play Dota all the time so I understand that you can have different builds for each character. I just wanted to get used to playing a bunch of the characters before I started messing around with the items. Plus trying to figure out different items mid-game just wastes time so I've been looking up stuff out of game. So now i think I'm ready to try different stuff and build champions how I want =)

When you hover over a skill, there's a number in parentheses (+0) if you have 0 AP; this number changes as your AP goes up to reflect the bonus damage that skill gets from AP. Some skills have no AP scaling. Look for the parentheses.