To install a Delta kitchen faucet, gather necessary tools such as an adjustable wrench and plumber’s putty. Remove the old faucet by disconnecting the water supply lines and unscrewing the mounting nuts. Apply plumber’s putty to the base of the new faucet and insert it into the sinkhole. Tighten the mounting nuts and reconnect the water supply lines. Check for leaks at the connections, and if any, tighten them further.