Disconnect and lift out an old kitchen faucet safely, with the water shut off and a basin wrench for the tight nuts.
Reach under the sink and turn both supply shutoff valves clockwise until they stop. If there are no under-sink valves, shut off the home's main. Open the faucet handle to let any pressurized water drain, then leave it open.
Place a bucket and towel under the connections to catch drips. Use an adjustable wrench to loosen the supply-line nuts where they meet the faucet tailpieces (turn counterclockwise). Have the towel ready — a cup or two of trapped water will spill out.
The nuts holding the faucet to the sink sit in a cramped space behind the basin. A basin wrench's pivoting jaw reaches up around them. Clamp it onto each mounting nut and turn counterclockwise until they spin free. Support the faucet from above so it doesn't drop.
Once the nuts and any retaining clip are off, pull the faucet straight up out of the mounting holes. Scrape off the old plumber's putty or silicone ring with a plastic putty knife and wipe the deck clean so the new faucet seats flat.