If your mat is lightly soiled, use a spray bottle, damp sponge, or terry cloth rag to apply a solution of two cups of water and four drops of dish soap. Rub the soiled areas. Wipe the mat with clean water; then rub with a dry terry cloth towel. Hang to air dry.
If your mat is heavily soiled, submerge it in a solution of warm water and mild detergent; use very little soap as any residue may cause the mat to become slippery during future use. Thoroughly handwash the mat and rinse in clean water. After squeezing out the excess water, lay the mat on a dry towel and roll the mat and towel together. Stepping on the rolled up mat will squeeze more moisture out of the mat and into the towel. Then unroll and hang to air dry.
Some mats also do well in a washing machine, use detergents sparingly and hang on the line to dry. Easy peasy.