Epoxy paint is often used to seal both concrete and wood floors. If you want to tile over concrete or wood, and there's a thick coat of epoxy on the surface already, you can tile right over it, but prepare first. Epoxy is hard, which is good for laying tile, but it's also slick and glossy, which isn't. De-gloss the epoxy, making sure none of it is coming up anywhere, and get it as clean and dry as possible before you start tiling.
Sand the floor, using your pad sander and 80-grit sandpaper. Start in one corner and work your way across, sanding it just enough to take up any loose surface material and to dull the shine. The floor should be non-reflective when you're done.
Mix a solution of 1 cup of trisodium phosphate to 1 gallon of warm water in a bucket. Thoroughly scrub the floor. Rinse-mop it with clear water. Let it dry completely for at least 24 hours.
Lay two lines across the middle of the floor with your chalk snapline. The lines should intersect each other. Use your carpenter's square to square the lines to one another.
Spread thinset mortar over several square feet at the intersection, using a notched trowel. Set floor tiles in place where the two lines meet, putting tile spacers between them.
Spread the rest of the mortar and tile, building out toward the walls. Put tile spacers between all the tiles as you install them. Use a tile cutter to cut the tiles by the walls, as necessary. Let the tiles set for a day, then remove the spacers.
Apply grout the floor, pressing grout into the spaces between the tiles with your grout trowel. Use a damp sponge to remove the excess grout.