Be sure that your computer is turned off.
To remove the dirt and lint from the body of your keyboard, hold the keyboard upside-down over a trash can and gently shake it. It is fine to give it a couple of gentle "pats" to remove the firmly lodged dirt or crumbs. Another method is to use a can of compressed air and give it a few shots to remove dirt and dust. Be sure to have a dust mask on if you are allergic to dust!
If you would like to clean between the keys, go get an old toothbrush and dampen it with a quick shot of Windex or similar. The just gently scrub between the keys. For cleaning the tops of the keys and the rest of the keyboard, go get a soft cotton cloth (an old sock works great). Dampen the cloth with a few shots of Windex or similar and gently wipe until clean.
Depending on your keyboard usage, it is a general recommendation to clean your keyboard approximately once a month. You power users may want to clean more frequent.