Plug an iron in and set it to medium. Wait three to five minutes for the iron to heat up and press the iron onto the laminate sheet where it's adhered to the wood.
Run the iron over the laminate beginning at the edge of the sheet and working your way inward to loosen the adhesive holding the sheet in place. Push the edge of a putty knife beneath the laminate sheet where you've heated the adhesive, breaking the bond between the sheet and the countertop core. Peel away the laminate sheet as you break the bond, working your way along the laminate length until you remove the entire sheet.
Dip a piece of cloth into lacquer thinner and rub the thinner into the adhesive on the rear of the laminate sheet and the adhesive on the wood core of the countertop. Allow the thinner to soak into the adhesive, loosening it from the surface. Scrape the adhesive from the two surfaces with a putty knife, applying more thinner as needed for difficult-to-remove sections. Wipe the surface clear with the thinner-dampened cloth to remove any residue. Wipe a second time with a cloth dampened with water to remove the thinner.
Apply a thin layer of contact cement onto the rear of the laminate sheet and the top of the countertop, using a paintbrush. Wait for the cement to dry to a tacky state, one where the cement is sticky but no longer wet.
Place a series of wooden dowels every foot along the countertop length. Set the laminate sheet over the dowels, cement side facing down. Align the laminate with the countertop.
Lower the laminate sheet to the countertop by removing the dowels from one end of the sheet to the other. Quickly adjust the sheet as you lower it into place, as you'll have only a matter of seconds before the contact cement becomes unworkable when the two sides meet.
Roll over the surface of the laminate sheet with a hand roller. Roll the sheet, beginning in the sheet center and rolling toward the edge to force out any air from beneath the sheet.