Determine what sealant is on the floor. Water-based sealants require water-based removers; petroleum-based sealants require petroleum-based removers. If the sealer is glossy, it is not water based. If you place a few drops of water on the tile and it absorbs into the tile, it is water based.
Prepare the area by cleaning the surface of any dirt, taping off areas you will not strip. Cover any cupboards or other objects in the room you can't remove so they will not get sealant remover splashed on them. If spot stripping, tape off the area that will not need sealant remover.
Pour sealant remover into the bucket or paint rolling tray. Work in small areas. Use a clean paintbrush to apply the stripper. Apply the stripper liberally, covering the entire area you will strip. Let stand for the time specified in the directions for the solvent.
Remove the solvent after the specified time. Use a scraper and rags to remove all the solvent and sealer. Work quickly because if the solvent dries, you may have to reapply.
Soak a clean, white terrycloth rag in some lacquer thinner, and wipe down the entire surface to remove any excess sealant remover. Scrub any areas in which the sealer did not come off with the stiff bristle brush. Repeat with remover solvent if the brush does not remove the small areas. Continue until you have removed all the sealer.
Clean the floor thoroughly, and apply new sealant according to the sealant directions.