The best way to give the laptop case a bath is with a damp sponge. Follow these steps:
Use standard dishwashing liquid, by mixing it at about 1 part detergent to 5 parts water.
Avoid using detergent that contains strong chemicals (acid or alkaline). Don't use abrasive powders.
Soak the sponge in the mixture, and then wring the sponge clean.
Gently wipe the laptop's case.
Ensure that the sponge is dry enough that it doesn't drip liquid into the laptop. Do not clean inside any disk openings or the PC Card slots. Never spray any liquids into those openings, either.
When you're done with the sponge, wipe off any excess moisture or dust by using a lint-free cloth.
You might also want to use cotton swabs to clean some of the gunk from the cracks.