If your countertops are the vineer type and are NOT curved, then you can either apply new vineer on top of the old or remove the old. If you do not have any holes or areas that the current is coming up, then just go over the old.
Applying new vineer is very difficult work and I won't even mess with that. you are dealing with contact cement and let me tell you one slip and the new stuff is permanently down regardless of right or wrong.
I would have a cabinet person come in and lay down new vineer for you.