It's a good idea to keep your mat in some kind of case or bag (even if you're backpacking) to give it some extra protection while it's not in use.
You should spot clean your pad with a mild soap and water to remove things like mud, sunscreen, bug spray, remnants of camp snacks, etc.
When putting your pad away for the season, lay it out and wipe down the entire outside of the pad, then let it air dry. Give it time to air dry both inside and out (in the case of self-inflating models) so that it won't grow mildew.