Turn off both water-supply valves under the sink. There is a valve on each line going to the faucet. Turn on the faucet to allow any remaining water in the line to drain and squeeze the sprayer head handle.
Follow the hose from the sprayer to the faucet. Some hoses connect with a quick connect fitting. If that is the case, pull the collar of the quick connect down with your fingers and pull the hose away from the faucet. If the sprayer hose connects with a compression nut, turn the nut counterclockwise with a wrench and remove the hose from the faucet.
Remove the weight that is on the hose with a Phillips head screwdriver. The weight is two pieces that clamp over the hose. Remove the screws on each side of the weight and pull the pieces off the hose.
Turn the nut securing the faucet sprayer head holder to the sink counterclockwise with a pair of slip joint pliers. Remove the nut and go to the top of the sink. Pull the sprayer and hose away from the sink.
Hold the sprayer head in one hand and loosen the hose securing nut with a wrench in your free hand. Remove any plumber's tape from the threads on the bottom of the sprayer head. Take the hose to the hardware store to purchase one that is the same length and has the same type of connectors (quick-connect or compression nut).
Wrap new plumber's tape around the threads on the bottom of the sprayer head. If your hose connects to the faucet with a compression nut, wrap the threads on the faucet with plumber's tape. Thread the new hose onto the bottom end of the sprayer head until the connecting nut is hand tight. Turn the nut an additional full turn with a wrench.
Insert the opposite end of the sprayer hose through the sprayer head holder and into the hole in the sink. Go under the sink and slide the holder securing nut over the hose and thread it onto the holder until hand tight.
Connect the end of the sprayer hose to the faucet. If you have the quick connect, pull down on the collar and insert the hose over the faucet nipple connection. Release the collar and pull down slightly on the hose to lock it in place. If you have the standard compression nut, thread onto the faucet threads and tighten with the wrench.
Place the hose weight around the hose 6 inches from the faucet connection. Secure the two pieces of the weight together with the retaining screws. Turn the water supply valves back on and check for leaks. Tighten the connections as necessary.