Wash the floor by mopping it with warm water and several drops of liquid dish soap. This scrubs away dust, dirt and grease stains. A clean surface benefits you when repairing cracks or adding a sealant. A pressure washer is another option, but is only recommended in severe cases of dirt or if the concrete is outdoors where the water dries and drains faster.
Remove oil stains and other blemishes from the floor using solvents such as trisodium phosphate or oxygen bleach. These are corrosive chemicals, so wear protective gloves, ventilate the room during use to avoid inhalation and follow all instructions on the packaging for best results. Rinse the floor again when you're finished. Let the floor dry fully before continuing.
Apply a concrete repair resin into any cracks in the floor with a syringe. Fill the crack with dry silica sand and then add more resin to the sand until the crack is fully filled. Let it dry for 15 minutes and then sand it down with fine sandpaper so the texture of the repair matches the floor around it.
Apply a sealer to the floor using a mop after finishing the repairs and letting them cure. Start in a far corner of the room and work backwards towards the door so you don't trap yourself in a corner where you have to walk over the sealer to get out. Wear shoes with proper traction because sealer is slippery when wet. Let the sealer sit overnight and then add a second layer for best results.
Wax the floor to give it a shine and to further protect it against staining and damage. Use a waxing mop to apply the wax much like you did the sealer. Three coats of wax usually work best. Strip and rewax the floors every few years to keep the concrete looking like new.