Lay the wrestling mats out on a clean surface. Do not lay them out on the floor where the wrestling meet took place unless the floor has already been disinfected. Make sure all wrinkles are out of the mats and that all folds in the mats can be accessed. You want to make sure the entire mat is cleanable.
Spray disinfectant on the wrestling mats. Bleach, peroxide or rubbing alcohol will all work. For every two squirts of this on the mats, you'll want to add one squirt of water, creating a ratio of 2:1. This is so the mat gets clean but so no disinfectant gets on the wrestlers' skin the next time the mat is used.
Leave the disinfectant and water on the wrestling mats for about 15 seconds, then wipe it off with paper towels. Make sure you wipe off all the disinfectant. The fumes from the disinfectant can be dangerous when inhaled and you don't want any stray cleaning agents on the mats the next time a match is scheduled. It won't soak into the material of the mat, but you want to get it off fairly quickly.
Dry the mats with a towel. Make sure they're completely dry. When they are, you'll want to turn the mats over and clean the other side of each. Repeat Steps 1 through 3 for the other sides--lay them out flat, then spray, wipe and dry them.
Store the mats in an upright position. This helps any excess water and disinfectant to roll off the wrestling mats and onto the floor where it won't harm anyone. Store them upright in order not to get one or the other sides of the mats dirty by keeping them on a floor.