Together, linoleum and vinyl constitute a class of materials known as resilient flooring; removing one is similar to removing the other -- and it's no picnic. If you can, install new flooring directly over old linoleum or vinyl to save yourself a difficult job. If the floor is old, it's important to [test the flooring, the backing and the adhesive] (http://www.Hunker.com/how_5084523_tell-asbestos-tiles.html) for asbestos before you do this job; if the test is positive, you need to hire a pro to remove the flooring.
Separate the Layers
Most resilient floor coverings are constructed in layers, and if you can remove the top layer, you have access to the under-padding and adhesive, which is more difficult to remove. Cut the flooring into strips with a sharp utility knife. Be careful not to dig the knife too deeply into the subfloor if it's hardwood -- you don't want to damage the wood. You should be able to work a stiff putty knife under the top layer and pull it off. If this doesn't work, insert the knife under the bottom layer and pull the all the layers off at the same time.
Get Out the Hair Dryer
You may be able to separate the layers more easily if you heat the flooring with a hair dryer set to maximum heat; if the flooring doesn't come off in layers, the heat may soften the adhesive and make it easier to pry the material from the subfloor. Don't worry about getting all the flooring and residue off at this point -- simply scrape and pull away what you can. This job is easier if the subfloor is concrete; wood is porous, making the adhesive bond stronger and more likely to resist your efforts.
Soften With a Solvent
If the flooring was installed recently, the adhesive may be water-soluble. Test a small area, and if water softens the glue, use small amounts of hot water in localized areas to help remove the glue. You may need to let the water sit for 10 minutes or so, but be careful not to damage any wood flooring or subflooring underneath with excess water, and dry the wetted areas as you go. Some adhesives, especially those used with older linoleum products, dissolve in mineral spirits. Because it's volatile and flammable, use mineral spirits more sparingly, wetting down one section of the floor at a time and scraping it before moving on to the next section. In most cases, you won't be able to remove all the glue residue at this stage in the procedure.
Scrape the Residue
If the linoleum was covering a hardwood floor that you want to restore, you can remove the glue residue when you sand the floor with a floor sander. A floor sander will also work on a plywood subfloor, but if the subfloor is concrete, other tools do the job more efficiently. Scrape off the residue with a reciprocating scraper, or use a walk-behind power scraper. A third alternative is to fit a floor buffing machine with a scraping attachment and run the buffer over the floor. You can rent all these tools at a home-improvement or hardware store rental outlet.