Remove throw rugs, furniture and other items on the floor of the room, or move the items to one side of the room to provide adequate work space on the other half.
Hold a hair dryer or a heat gun over the vinyl, and move it back and forth over a seam between tiles until the adhesive softens.
Slide a putty knife under the seam and lift the edge of the tile.
Grip the edge of the tile with vise grips. Heat the tile with the heat gun or blow dryer over the field of the tile. Pull on the vise grips to peel the tile off the floor. If you meet resistance or the vinyl begins to rip, continue to heat the tile until the tile peels away from the floor.
Scrape the adhesive off the wood surface with a plastic putty knife. Heat the adhesive with the hair dryer or heat gun, and continue to scrape until only a light layer of adhesive remains.
Move to an adjacent vinyl tile, and repeat the removal techniques. Continue to move tile by tile over the floor, heating the edge, gaining a grip, heating again and peeling the tile off the wood until no vinyl remains on the wood.
Swab a 4-by 4-foot section of the floor with a citrus-based adhesive remover that is safe for use on wood. Let the remover soak into the old adhesive and soften it for 10 to 30 minutes, depending on the remover manufacturer's directions.
Wipe the floor with a large, disposable rag to remove the adhesive and remover. Move to the next 4- by 4-foot section, spread the remover, let it sit and wipe it away with a rag. Continue to clean the old adhesive residue off the floor until no adhesive remains on the wood.
Fill a bucket with water and 1 teaspoon dish soap. Submerge a sponge mop in the water, and squeeze the water out of the sponge, so it is damp. Mop the floor to remove the remover residue. Dry the floor immediately with a towel.