Easy to do by hand. On a shop fabricated counter, the end would go on first with the top surface overlapping it so water would drip over the edge and not into the seam between the top and cap. With prefabricated tops, there's no choice but to glue the end on last. Make sure you use enough contact glue on both surfaces and wait til it's tack free before attaching the cap. Then use plenty of pressure to get it to stick well. A rubber mallet will do or even pushing on the corner edge of a 1x2 or similar stick where you can get a lot of leverage and pressure per sq in. Use a wide metal cutting file, not a wood file as a wood file or rasp will leave a rough edge. With the counter top lying flat, file upward at an angle with the top laminate, also holding the file at an angle and not perpendicular with the top. Then take long even strokes, lifting the file on each back stroke so as to not chip the end cap by filing backwards. File until the edge of the end cap is even with the top laminate, taking care not to file into the top laminate. Even with a router, the pros use a file to eliminate the chatter marks left by the router bit. If you have a particleboard core and the counter is subject to a wide range of humidity conditions, you may find the end cap you applied might project a little above the counter laminate as the core changes dimensions. A few strokes with your file will fix this if needed.
Glen