Steps:Demolition. Check to see if you can pull up the old floor. If possible, pull it up and remove it. If not, you may need to simply install over the old flooring.
Install new underlayment. For a sheet vinyl floor like this, luan is the best choice for underlayment. It's smooth, easy to use, and inexpensive. Cut the luan to fit, and screw it down every 8" using 1-1/4" drywall screws.
Smooth the underlayment. Using a self-leveling floor filler, fill the screw holes and seams in the luan. Any imperfections in the underlayment will show through in the floor.
Template, step 1. Make a template for the floor. Using brown paper, cover the entire floor by taping overlapping pieces together. Cut holes in the middle of the paper to tape the template to the floor. Stay about 1inch from all edges. Next, take a 2-inch wide straight edge (or the leg of a framing square) and trace the entire room onto the template by pressing the straightedge against the wall, and drawing onto the template.