Clean the shower floor well using detergent and cleaning rags. Eliminate any soap, grease and dirt from the tiles and grout. Allow the tiles to air dry completely, about 6 hours. Place the drop cloth on the floor next to the shower to protect the flooring you don't want sealed.
Fill the bucket with epoxy sealer. Dip the sponge mop into the bucket and apply it to the farthest corner of the shower floor. Mop the sealant onto the ceramic tiles with smooth and even strokes.
Rewet the mop with the sealant as needed. Set the mop down in the same area you left off until the entire shower floor is covered with an even layer of sealant.
Allow the sealant to dry completely, about 24 hours. Place a fan in the bathroom so it blows onto the shower floor to ensure adequate drying.
Apply a second coat of sealant if the manufacturer's instructions require it. Some nonslip epoxy sealants require two coats for the most effective results. Allow the second coat to dry for 24 hours and use the fan if needed.