Hand wash with very hot water and ordinary dish washing soap (not lotion/moisturizing soaps). Heat the water, pour into a bucket with soap and immerse the face mask(s). If heavily soiled, add an oxygen cleaner (for example, Oxyclean) according to the package instructions. Agitate, soak. Rinse very well in plenty of water. Squeeze well. Let air dry.
Machine wash, hot water, using laundry soap that DOES NOT contain fabric softeners; a powdered detergent is preferred. If in any doubt, choose a powder detergent. Add an extra rinse cycle as needed. Air dry or machine dry on a warm cycle. If machine drying, consider using a mesh bag to prevent damage to elastics or ties.
Other sanitizers could be used with soap/detergent, when washing by either hand or machine. These are household bleach, liquid laundry sanitizers (for example, Pine Sol), quaternary ammonium salts, such as found in many over-the-counter cleaners (check the label). Follow the label directions accordingly.