Please note that while I show a corded keyboard here, you can follow these steps with a cordless keyboard as well.
Step 1: Open The Keyboard
After they're all out you'll have to carefully pry apart the two halves of the keyboard. They may be stuck together pretty well, so don't be afraid to use A BIT of force. The best way to do it, is to pry open one corner and then work your way around the keyboard.
*TIP: Don't pry the keyboard open on your lap. When it opens all the dirt that's inside will fall out onto you.
*TIP: If you're trying to pry the keyboard open, and it seems to be "sticking" in one place, make sure you've removed all the screws. Be sure to check under the labels, and the rubber feet.
Step 2: Inside The Keyboard
To just clean the gunk out from between your keys, all you need to be concerned with is the half with the keys. If some letters aren't typing, you'll need to deal with both halves.