Mop the asbestos tile floor with hot water and a tile floor cleaner. Removing all the dirt and grime from your tile floor before applying the epoxy is important. Otherwise, the dirt and grime will become trapped under the layer of epoxy.
Push the mop across the tile flooring again but this time use only water. This ensures that all traces of the floor cleaner are removed.
Wait for the floor to dry. Mix the epoxy floor kit as instructed on the product label. Typically, this involves combining an epoxy paint with a hardener. This Old House warns that once you mix the epoxy, you have a maximum of two hours to use it.
Slide a pair of chemical gloves over your hands. Put on a pair of goggles, a mask and a pair of rubber boots. This will protect you from the chemicals in the epoxy kit. It is also a good idea to ventilate the room while you are applying the epoxy.
Brush the epoxy over the asbestos tiles with a paintbrush, starting at the back of the room and working toward the front.
Wait 12 hours before applying a second coat of epoxy and 24 hours before allowing foot traffic to commence on the flooring.