Take off the cove molding along the soffit with a pry bar.
Unscrew the cabinet unit from the soffit and remove the cabinets.
Throw away the old cabinet doors, molding, old hinges, etc.
Note: You'll need to rent a 6-yard dumpster for all of the trash removal. A dumpster usually rents for approximately $200.
Shut off the water and cut the copper water-supply line to the refrigerator.
Turn off the main gasline to the stove and disconnect the supply line at the back of stove.
Remove the appliances, and note that it's best to use an appliance dolly for the job.