Summarize:

Most steam mops have removable fabric pads that are easy to clean and maintain. Make sure the mop head is cool enough to touch, and remove the pad. Then wash it on a normal cycle with every-day laundry detergent/ Try to put your mop pad in with other loads of laundry so that you aren't washing it by itself. This is more environmentally friendly, and also less harsh on your mop pad. Clean the tank or reservoir of your steam mop by emptying it out and wiping it down with a damp dish towel or rag. Change out dirty cloths as necessary to avoid re-soiling the inside of the tank. Use a dry towel or rag to wipe down the whole surface of your steam mop after every use. This helps wipe away built-up debris, and wicks away any moisture left behind after mopping.
Wash the pads in the washing machine after every use. Wipe out the reservoir. Clean the surface of your mop.