Sweep the concrete floor to remove dirt and debris.
Attach 40-grit polishing wheels to a concrete grinder as directed by the manufacturer. For a full floor job, a walk-behind grinder is the most effective; for a small patch on a floor or a wall, use a hand-held grinder.
Place the machine on the concrete so the grinding wheels make contact. Turn on the grinder. Immediately start to move the grinder in a back-and-forth motion and move the grinder across the surface. Move fast enough that the grinder doesn't leave swirl marks. When the area is even, turn off the grinder.
Replace the 40-grit grinding wheels with 80-grit wheels. Grind the entire surface again.
Vacuum the concrete dust with a wet/dry workshop vacuum. Sweep up any remaining dust.
Remove the 80-grit grinding wheels and replace them with polishing pads. Polish the floor with the same technique as with the polishing wheels. For a glossy shine, start with an 800-grit polishing pad, apply a coat of polishing compound with a microfiber mop and switch to a 1,500-grit to finish.