Remove everything from the basement floor.
Vacuum all of the dust, dirt and debris from the concrete floor with a wet/dry vacuum. Focus on corners and the areas around your furnace, oil tanks and any other equipment where dirt could build up.
Scrub the floor with a wire brush and mineral spirits to remove any grease buildup, giving special attention to areas around oil tanks and oil furnaces. Any oil or grease let on the floor will allow the sealer to peel up over time.
Apply an acid etch to the flooring with a bristle broom to remove any remaining grease and oil. If your basement does not seem to have any excess grease or oil, you can forgo using the acid etching. If you do use acid etching, thoroughly clean the floors with fresh water and allow the floor to fully dry before moving on.
Fill in all of the cracks and missing concrete you can find on the floor with a concrete patching. Wait for the patching to dry and then sand the patching flat with the floor with an orbital sander. Vacuum the floor to remove the sanding dust.
Mix the epoxy concrete sealing paint, and then roll the paint onto the floor with a paint roller. Apply at least two coats of sealer, and allow a 24-hour drying period after each coat.