Use a concrete filler epoxy and a putty knife to repair any cracks or holes in the concrete floor. Allow the floor to cure, according to the instructions on the package, before polishing.
Sweep or vacuum the floor before polishing it. Dirt and debris can scratch the floor during the polishing process.
Rent a floor grinder from your local home improvement store. To polish concrete, you will need diamond discs rather than standard sandpaper. Start with the coarsest grain available and continue with progressively finer grains until you achieve the polish you desire. The lowest grit is 80, and the amounts double for the grain as the discs become finer. The finest grain available for this type of diamond disc is 3000 although the 1500 grain may give you the smooth polish you want on your concrete floor.
Apply a sealant designed specifically for concrete flooring. Pour the sealant into a paint tray and use a roller with a long handle to apply it. Each brand of sealant requires a different amount of time to dry, and some require additional coats.