Start by removing the drawers and clear out all the cabinets to avoid filling them with dust and debris. Tape the cabinet doors shut.
If there is a window above the countertop, it may be necessary to remove the window casing and stops around the window in order to pull out the old backsplash. Prevent damage to the casing so it can be reinstalled later.
Below the sink, turn off the water supply valves to the hot and cold water lines and use an adjustable wrench to disconnect the faucet water lines. Have a towel handy to catch the water that drains from the pipes.
If the water supply nuts are corroded and difficult to remove, cut the copper faucet pipes with a reciprocating saw or tubing cutter. Apply penetrating oil to the remaining nuts and leave for later, when they will be easier to loosen.
The sink often can be removed with the faucet and sink-top accessories attached. If there is not enough clearance, use a basin wrench to reach up behind the sink and remove the nuts securing the faucet handles and faucet spout tailpiece.
Remove the countertop backsplash by prying out sections, starting in the middle.
Check below the countertop to see if there are any screws or retaining hardware fastening the counter to the cabinets, and remove them. The countertop can now be lifted away and discarded.
If the countertop is very large or an unwieldy shape, such as with L-shaped tops, remove any hardware fastening separate sections together, or cut the countertop into manageable pieces with a reciprocating saw. Before cutting, pull off any metal trim along the countertop or backsplash edge. Use a fine tooth bimetal blade and wear safety glasses when cutting through laminate surfaces.