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.
Step 3: Cleaning the Circuit Boards
Step 4: Cleaning the Keyboard
After all the keys are out, simply rinse them and the front of the keyboard (not the circuit boards) off in a sink or tub. Be sure to dry them off well.
*TIP: Write down the order of the keys, or take a picture so that you can put them back in properly.
Step 5: Putting It All Back Together
First you have to put all the keys back into their proper positions (you do remember where that is don't you). To do this, simply line each key up with the hole it left, and press it back into place. It will click when fully inserted. If you chose to remove the space bar, be sure to insert the spring properly. Unlike the other keys this one should spring back when pressed, even with the keyboard apart.
After all the keys are back in it's time to put the two halves back together. To do this, lay the half with the circuit boards on a hard surface, and place the half with the keys on top of it. Then gently press down on the top half, until it clicks together. Be sure to go all the way around the keyboard to make sure it's together properly. Once it is, flip the keyboard over and replace the screws (again, "Lefty loosie, righty tighty"). It's best to put the four corner screws in first, followed by the center before replacing any other screws. This is so the back won't bend and make other screws more difficult to get in.
Please note I am not responsible for any damages or injuries sustained while following these instructions. While I strive to make all of my guides as safe as possible, you follow them at your own risk.