Turn off the water in your house by closing the main water valve. Turn on a faucet, if possible at a lower level of the house than the kitchen, to drain out any leftover water from the pipes.
Put a bucket under the sink’s pipes. Use a pipe wrench to turn the nuts at the pipe connections counterclockwise, separating the pipe sections from each other. Turn the connections at both ends of the water-supply lines under the sink counterclockwise with a basin wrench, removing the supply lines as well.
Cut the caulk between the edge of the sink and the counter, as well as the counter and the wall. Lift the sink out of the cutout in the counter and set it aside. Slide out all of the cabinet drawers and remove the screws holding the cabinet door hinges in place, then setting aside the doors and drawers.
Look under the counter for any retaining screws that hold the counter to the cabinets. Remove all the screws you find. Insert a pry bar between the counter and cabinet, and lift the counter up to separate it from the cabinet.
Cut through the caulk at the counter’s seams with a utility knife and remove the separate sections from the cabinets. If some sections are too large to remove, cut the sections into pieces with a reciprocating saw, being careful to not damage the cabinets.