removing a counter top is pretty easy once you have removed the sink and cook top and anyother appliance that is built in to the countertop.
There should be some special metal fasteners all around the underside of the counter top that pulls the top to the actual cabinet frame. They will only be assessed when the drawers are removed and the cavity is open. Its difficult on the back to find these and loosen them. Should be one every two feet or more.
Then you might have a caulk line that you need to cut with a box knife. Then it should lift off. What to do with the pieces of refuse is beyond me.