Clear off any appliances or other items you keep on top. Remove top drawers and empty cupboards if necessary to give you room to work.
Turn off the water, remove all screws holding the sink in place and remove the sink. If the sink is glued to the counter top, gently slide a putty knife around the perimeter of the sink.
Cut the caulk between the backsplash and the wall with a utility knife. Slide the putty knife between the wall and the backsplash and use a pry bar to pry it off where the putty knife is inserted. Try to pry the backsplash away from the wall at points where there is a stud in the wall. This will help prevent damage to the wall behind the backsplash.
Remove all screws holding the counter top in place. Some counter tops are held in place with only screws, so you can test to see if your counter will come up once you have removed the screws by gently lifting it.
Slide the putty knife between the cupboard and the counter tops. Do this wherever there is glue to minimize damage to the cupboards when you remove the counter tops.
Lift the counter tops off the cupboard with the help of another person. If they still will not come off, use a pry bar to gently pry the counter tops off. Place the putty knife between the pry bar and the tops of the cupboard to reduce damage to the cupboard.