For exact directions, be sure to read the instruction manual that came with your particular pump. (If you lost it, you may be able to find a copy online from the manufacturer’s website.)
For most pumps, you’ll need to disassemble the parts after each pumping session, wash the parts that come into direct contact with your milk in warm, soapy water, and leave them out to air dry. Most pump parts can go in the dishwasher (check the instructions) or can be steam sterilized (Medela sells Quick Clean Micro-Steam Bags) or wiped down with breast pump cleaning wipes. Different pumps require different handling of the tubing. (Some have a valve that blocks them from the milky parts so they won’t need to be cleaned; others don’t. Again, check your instructions.) The pump device itself doesn’t usually require cleaning, since it doesn’t come in contact with your milk. If you spill on it, just wipe it down with a damp cloth.