Turn off the water and gas to the countertop sink and cooktop. Locate the shutoff valves under the counter. Turn the shutoff valves to the off position. Test the lines to be sure that the water and gas are turned off by attempting to turn on the sink and stove.
Disconnect the supply lines from the shutoff valves using an adjustable wrench. If your cooktop is electric, turn off the electrical power at the main breaker and disconnect the electrical line.
Disconnect the P trap from the drain pipe under the sink using a plumber's wrench.
Check underneath the cooktop to see if it is screwed into the counter. If so, unscrew it with a screwdriver.
Pull the cooktop up and out. If it won't come out, run a paint scraper under the edge of the cooktop around its perimeter to disconnect any adhesive, then try again to remove it. Repeat this process with the sink. If the sink is held in by tiles, you'll need to pry up the tiles and mortar around the sink before taking it out. Remove the tiles and mortar with a paint scraper.
Remove any drawers from the cabinets. Unscrew cabinet doors and set them aside. Keep the screws to reuse them later.
Check underneath the countertop for screws that may be holding the counter to the cabinets underneath. Unscrew the countertop.
Wedge a pry bar or crow bar under the edge of the counter and pry it up. The counter may come up relatively easily. If you experience trouble disconnecting the countertop, try cutting the countertop away from the cabinets beneath it using a jigsaw.