Hi Tom, first a few questions. Does the existing countertop have backsplashes or does it butt up to tile? Second, is the top a straight run, or does it make "any" corners/angles?
The reasons I ask is that a top with only backsplashes is VERY easy to remove, and corners don't really have any effect. But if it butts up to tiles, and especially if it has a turn/corner on it, then things get more tricky as you don't want to damage the tile.
In all cases, the top will either be secured in place either with screws, glue, or chalking, or a combination of those items. First thing to do in any case, is to use a utility knife and cut all surface chalking and any places that the top may be adhered to painted surfaces (keeps it from tearing up surrounding surfaces, i.e., painted walls/cabinets). That done, remove the sink, etc., screws... use a 5-in-1 tool to breakup any glue/chalking on the underside of the top.
Okay, that's the start of the job. Now the real fun begins. If the top has a turn/corner in it and is butted up under tile, then most likely you will have to cut the top and take out in pieces... unless there is a seam in the corner (and if you're VERY lucky) and it's not glued together. If there is a seam, check under the seam to see if there are some bolts holding the two pieces together. If the top simply has backsplashes, once you remove them it doesn't matter if there is a corner or not.
Okay, now that everything is free you simply start working the top up and down in small amounts and eventually it will come free and slide out. You will need a helper if the top is very big... one of you at each end doing the work.