Wedge the flat tip of a crowbar beneath the existing edging. Tap the end of the crowbar with a hammer. This pushes the flat tip between the laminate edging and the counter frame. Pry the existing edging away from the counter frame.
Run a flush tip router along the rough edges of the counter frame. The flush tip router sands away any laminate glue that remains, ensures that all of the edges are even and leaves a rough surface for the new edging to adhere to.
Affix a laminate trim blade to your power miter saw. Position the tip of the blade at an angle against the 90-degree joint between the countertop and its edge. The angle you choose is solely a matter of personal preference but determines the angle of the finished beveled edge.
Measure the length and width of the edging. Include the angle in your measurements. Cut a strip of laminate to size with a utility knife. Dry fit the laminate strip against your countertop's new beveled edge to ensure that it will fit properly before applying adhesive.
Apply a generous amount of carpenter's glue to the back side of the laminate strip.
Align the laminate strip's edge with the countertop's edge. Press the strip down firmly across the edge, bending the laminate over the beveled edge. Apply filament tape over the laminate strip every 3 inches to hold the strip in place while it dries.
Remove the filament tape after the glue dries. This takes approximately 10 minutes. Check above and beneath the new edging for glue that leaked out from beneath the laminate strip. Clean away any excess glue with a clean washcloth dipped in mineral spirits.
Run your fingers along the top and bottom edges of the laminate strip to locate rough spots. Gently smooth away any rough spots with a file.