Old-style or new-style case?
For the new-style case, there are clips all around.
The old-style case should come open quite easily now. You just need to push the circuit board to the front, then it will separate from the top case which can subsequently be taken off. Dead easy once you get the hang of it. When you take out the PCB, be sure to remember how the cable went into the strain relief.
The case parts can be cleaned easily with water and a bit of dish cleaning liquid, same goes for the cable. For the keycaps I would recommend sixty's method, i.e. use denture cleaning tabs in a bowl of water. Do not attack the circuit board with water, just dust it off with some big brush.