Alright, first of all, make sure you take a picture of your keyboard before you start.
Otherwise you won't know where the keys go and life sucks. Here's my keyboard.

Pretty ugly, yes I know.

Now flip the board over, remove all the screws and you might see something like this. Remember every board is different so be prepared to have a 100 rubber cups come flying out at you if yours doesn't have this nice metal plate like mine did.

If you have a cool plate, remove it and you will see something like this.

Remove the plastic circuit board and dump all the cups out of the way for now.

Now start removing the keys. Use something narrow and sharp to press each one through.

Now you can see all the crud under the keys.

Clean it off. I used a garden hose since it's all just plastic.

Put all the keys in a jar.

Add hot water and soap. Shake it up.

Now dump all the keys in a strainer and rinse them off with water.

Start putting all the keys back in according to the picture you took before you started.

Once you have all the keys in, flip the board over. You need to prop it up so that all the keys hang down and none are being pressed up. I found two power supplies work nice. Now put all the rubber cups back in.

Put the plastic board back in and make sure everything lines up perfect. If even one connection is off chances are the whole keyboard won't work.

Put the rest back together and you're done. Here's how mine came out.

Keyboard is now nice and clean.

Number Pad looks great too.