Place the edge of a putty knife between two carpet squares and begin sliding the knife under the first square. As the carpets lifts, slide the putty knife over until one side of a square is unstuck from the linoleum and you can grab it.
Grab the edge of the square and peel it off the linoleum. Use the putty knife as necessary to separate any areas that are difficult to remove.
Remove other squares in the same manner until you are finished.
Remove the adhesive residue left behind to get a smooth, clean surface before reapplying another tile or another type of flooring. Several solvents are available to do this. For example, spray a spray lubricant on the adhesive, wait 10 minutes, then scrape it off with the putty knife. You can also rub off the adhesive with a rag moistened in mineral spirits, rubbing alcohol or vinegar. Alternatively, sand the adhesives until the surface is smooth enough to apply another tile or type of flooring. You can also heat the glue with a heat gun for about 30 seconds, then scrape it off with a putty knife.