Blast the stuck-on adhesive with a heat gun. If you don't have access to a heat gun, a hair dryer may be a useful substitute. Keep the heat gun moving over the glue while you scrape it with a razor blade.
Scrape up as much of the glue as you can. If you get to a point when the heat gun is no longer effective, switch to using solvent.
Apply an adhesive solvent, such as acetone, directly to the glue. Allow the solvent to sit for about 10 minutes or as directed by the manufacturer.
Scrub the adhesive with the razor blade, a stiff-bristled scrub brush, or a piece of steel wool. If you notice that the adhesive is softening, use the heat gun in conjunction with the solvent for better results, but only if the solvent you are using is not flammable -- read the warning label on the package for specific information. If you are unsure about safety, don't use the heat gun with the solvent.
Continue scrubbing at the adhesive until it is completely gone. If you reach a point where nothing you try seems to work, sand the adhesive down by hand.
Sand the adhesive with 100-grit sandpaper until it is completely gone. Check your work often to make sure you aren't sanding the concrete. Wipe the floor with a damp cloth when checking your progress.
Scrub the floor with trisodium phosphate mixed with hot water. Use 1/4 cup trisodium phosphate for every gallon of water. Rinse the floor thoroughly and suck up the excess liquid with a wet/dry vac.
Allow the floor to dry completely. Inspect the floor for residual adhesive and determine whether further action is necessary. If the damage from the adhesive only covers a small area, consider covering it with a small area rug.
Paint the floor if the damage from the adhesive covers a large area. Staining is not advisable because it will bond to the damaged areas and may make the discoloration stand out even more. Paint will cover the surface of the concrete.
Paint the concrete with a primer. Use a paint roller to make the job go faster. Use a paintbrush for the edges and corners of the room before painting the main area with the roller. Allow the primer to dry.
Apply the paint over the primer using the same method. Use uniform strokes that go in the same direction for best results. Allow the paint to dry. If desired, apply additional coats of paint.
Apply a concrete sealer designed for use with the paint and primer you used. For example, if the primer and paint were water-based, the sealer should also be water-based. Concrete sealers vary by manufacturer, so read the informational label for specific information on safe handling, application and drying.