Remove the floor trim using your hammer and pry bar. Don't break it. Set it aside.
Take up whatever flooring is currently in place, if necessary. Flat, hard surfaces like wood, tile (with no contours to it) or hard vinyl can stay in place. Carpet, padded vinyl or anything else that has "give" to the surface has to come out.
Thoroughly clean the bare floor with household floor cleanser. Let it dry completely.
Use a chalk snap line and square to divide the floor into four quadrants, snapping to intersecting lines from the middle of each edge of the floor to the middle of the edge across from it. Lay the square at the intersection as you snap the second line to ensure they are perpendicular to one another.
Put the wax paper backing off one tile. Press it firmly to the floor at the intersection, so the two adjacent edges of the tile are bordered by two of the lines. Set it firmly, putting weight on it with both hands.
Pull the paper off the second tile. Set it alongside the first tile, butting the edges tightly.
Repeat the process each tile, working your way out from the middle of the floor toward the edges.
Cut tiles to fit along the perimeter of the floor using your utility knife. Make the cuts by running the knife alongside your square to score the surface, then snapping the tile at the line. Cut it to leave about ¼ inch of space between the edge of the tile and the wall.
Reinstall your floor trim using your hammer and trim nails. The trim will cover the spaces around the perimeter.