With any luck if it's a new or linoleum and has no asbestos in it and the installer didn't use the correct adhesive, the stuff might just lift right off the floor. If not, and it comes up difficult, you might want to lay a 6 ft long straight edge of some sort on the floor and make a slice every 4 inches. Then using a handheld razor scraper, you try and peel up one 4-in section at a time. Once you score a line with a straight edge you can set this straight edge aside and make a couple of more cuts to get deep enough to go all the way through the material. It's less than 1/8 of an inch thick not a quarter inch thick. If it's warm in the house it will cut much easier than if it's cold.
Just try cutting a 2-in wide by 6 in wide strip starting at the doorway and try and scrape it up with a semi-sharp chisel. That will give you some indication as to how much effort it will take to remove the rest of the floor.
