Once a countertop has had the contact cement on it, it is difficult at best to install a new formica surface on it. The effort you will spend on trying to preserve the existing substrate, combined with the likelyhood that you will damage it, that the new surface will not make solid contact, and that the existing substrate is water damaged in some way (likely) outweighs the cost of just ripping the sucker off and starting from scratch with new substrate.
Other people may disagree, and that is their right. This is my opinion.
There are several posts on the board about how to do this, just make sure that your new self-edge (the part of the counter that hangs down in front) is not so low that you can't open the drawers or cabinet doors, and screw your new countertop to the cabinets from underneath, which hopefully is how the ones you have now are attached, or you will see why you should do it that way when you go to remove the existing counter.