I turned over vinyl to paint on the back side. I also sanded (with a fine sandpaper block) the edges of cut to size piece of vinyl to rid the sides of any loose vinyl pieces and rough look/feel to them.
I placed the vinyl piece on a thicker piece of plastic (for a drop cloth) so that I would be ready to paint.
I applied primer on the back side of the vinyl piece and the good side will be against the floor. I also put primer on the sides of the vinyl since they will be visible from across the room when looking at this mat on the floor. I ended up applying 2 coats of primer (used Kiltz) to seal the vinyl.
I had the paint I used for the trim in our home (Sherwin Williams Pacer White, Latex in satin finish) and used this (so that my whites would not clash in the room) to apply 3 coats of paint to the top that is getting used and a couple of coats to the sides (edges) too.
I let this all dry over night (the primer, Kiltz leaves the vinyl feeling tacky and damp, but is OK). Ready for the next step. Step 2 HERE