Probably the best advice I can give is:
Lay the laminate on top of your counter, and trace the perimeter of the counter on the underside of the new laminate with a pencil or felt pen.
Score down the outside edge of that felt pen line with a plastic laminate knife (which costs about $5 or so at any hardware store). Once you score it deep enough, it will break along that scored line when you bend it.
Sand down the old laminate and spread contact cement on it, allow time for the contact cement to dry, and cover it with strips of wax paper. Spread contact cement on the underside of your new laminate. (Before doing this, I'd try sanding down some sample chips of laminate and sticking sample chips of laminate to them with contact cement. I don't know for certain that contact cement will bond to the top of plastic laminate. It'll bond to the bottom, but it has to bond well to both before you can contact cement plastic laminate to plastic laminate. Otherwise, you might be best off removing the old plastic laminate and bonding the new plastic laminate to the plywood under your old plastic laminate.)
Place the new laminate on top of the wax paper, contact cement side down. Use a pair of clamps to clamp one edge of the new laminate down to the counter so it doesn't move during the gluing process. Lift the opposite edge of the laminate and remove as many wax paper strips as you can. Press the new laminate down onto the exposed contact cement. Remove the clamps, pull up the opposite edge of the new laminate and do an encore peformance so that the new laminate is glued down.
Now, use an ordinary steel file to file the new laminate down so that it's flush with the old counter top. Alternatively, use double sided tape to stick some of the thinnest sheet metal you can find to the edge of the counter, and cut the new laminate close to flush with the old counter using a hack saw or jig saw fitted with a metal cutting blade. Then remove the sheet metal and file the new laminate down flush with the old counter with an ordinary file.
Metal cutting blades have closely spaced teeth, which is what you need for a thin material like plastic laminate.
PS: The "right" way to do this is to cut the new laminate considerably larger than the old counter, glue it down, then trim it down with a bearing piloted router bit so that it's the size and shape of the old counter, and then file the edge down as necessary with an ordinary file. Normally, you would laminate the edges of the old counter top first, then laminate the top. However, a router or laminate trimmer is gonna cost at least $100. A bearing piloted bit will be another $25 at least.
I own a small apartment block, and I removed the old plastic laminate from my plywood counter tops and installed new prefab plastic laminate counter tops over the old plywood. I think that's a better way of doing this job than laminating over the existing laminate or replacing the existing laminate. You can see what this looks like on my web site at:
http://www.ilos.net/~nkelebay