If your laminate countertop is starting to lift up, it is an easy fix to repair it. Simply apply contact cement to both surfaces, the underside of the laminate and the countertop and press the laminate back into place.
If the edge of your laminate countertop is damage, and you are unable to repair it, remove the edge with a putty knife. Using a heat gun or an iron will help to soften the glue and make it easier to remove. After removing the damaged piece, sand the surface, apply contact cement and apply a new edge. If you are unable to match your countertop, be creative. There are many different laminates available, make the edge different.