i second gary's opinion, use carpet cleaner (spray on foam stuff) work in gently and then wipe off and leave to dry in a warm place, that way its really unlikely that you'll get the underside 'wet' at all
If you have a wet vac you could also suck the moisture out after cleaning then leave to dry to speed up the process
'Shelby' - 1985 bronco XLT, 351W C6, Limited slip 9 inch