How can I extend a granite countertop?

Use a Wooden Edge..... A wooden molding can be glued to the edge of the countertop using two part epoxy. Select a molding that is at least as wide as the counter is thick, taking into consideration the thickness of the granite. Glue the edge down first using two part epoxy and painters tape to secure it in place until the epoxy is cured. Stain the edge the same color as the cabinets to help blend it in with the rest of the kitchen. ***** Use a Decorative Tile Molding..... Many types of tile are designed with decorative rail moldings. This includes some colors of granite, along with marble, slate, travertine, glass and ceramic. Choose a decorative molding that picks up one of the colors in the granite or in the backsplash tile to coordinate it. Use two part epoxy to secure the moldings to the edge of the counter and painters tape to secure it in place until the epoxy is cured. ***** Use a Metal Edge..... If your kitchen is contemporary in style, consider using a metal edge to finish the granite and the counter front. Look for a metal edge designed for use on counters and stairs. Part of the metal strip will install below the edge granite. The visible portion of the strip will curve out from under the granite and down over the front of the counter. Metal strips are available in numerous finishes, including stainless steel, nickel, chrome, oil rubbed bronze and even nonmetallic colors such as black or white. Choose a finish that is already present in the kitchen for the most cohesive look. Glue the edge down first using two part epoxy and painters tape to secure it in place until the epoxy is cured.

I agree with William - use a wooden edge and even reclaimed wood would be a nice touch.