Bruce, First question that comes to mind is why are you removing the linoleum? Today, you can get adhesive to put down most anything over old linoleum. But, if for some reason(s) (ie: bad spots in current areas or not adhered 100% in all areas) ...and you are forced to remove the linoleum, unfortunately, there is only one way and it is extremely labor intensive. 1. Score the linoleum with a sharp utility knife. Do this in long "cuts" approx 6" wide. 2. Pull off the top layer of the linoleum. 3. Then (here's the hard part), with a very sharp floor scraper, you must literally scrape off the rest of the linoleum backing and the old adhesive.
We have found the Red Devil wall paper scraper to be the most effective (we've done this 4 times in the last 8 years). Buy lots of extra blades. Beware of the blisters as they are coming!!! good luck terrya