Washing your makeup sponge everytime after use will prevent bacterial and also let the makeup sponge last longer. If you see your sponge lost its original shape, smell odds or starting to shred at the edge, replace it with a new one. Normally, I would discard my makeup sponge after using it for a few times.
Wash your makeup sponge with antibacterial or regular soap. Allow your sponge to air dry after that. Store your makeup sponge in small plastic containers that are specially made for sponges.
Suggestion: Buy replacement makeup sponges from pharmacies where they sell it in large quantities. This will let you save more money than buying over cosmetic counters.