Take the dresser outside. The spray adhesive can get everywhere and smell really strongly, so it is best to do it outside.
Take the drawers out of the dresser, and remove the drawer pulls with the screwdriver.
Cut pieces of fabric roughly the size of the drawers, as well as the top and sides if you are covering those. They do not have to be the exact size, as you can trim them up later. Just make sure they are large enough to cover each.
Spray the adhesive on the front of one of the drawers.
Carefully lay the fabric over the adhesive. Go slowly, and smooth out any wrinkles before they can stick too much to the drawer.
Repeat with the adhesive and fabric for each drawer and the top and sides of the dresser. Do one at a time, so the adhesive does not have time to dry before putting the fabric on top.
Trim the fabric, so it matches the edges.
Cut a small "X" with a razor blade over the place where the drawer pulls screw into the drawers. You should be able to feel where this is with your fingers.
Screw the drawer pulls back in place.
Allow the spray adhesive to dry the correct amount of time. The time frame is different for different brands, so check your spray.