Turn off the water supply valve on the wall below the kitchen sink. To turn off the valve, turn the handle clockwise until it's tight.
Place a bucket below the water supply valve to catch any water remaining in the line.
Loosen the nut on the end of the water supply line connected to the water supply valve using an adjustable wrench. Continue un-threading the nut until the water supply line falls off of the valve. Allow any water contained inside of the line to fall into the bucket below.
Loosen the nut on the bottom of the brass valve outlet on the bottom of the faucet and remove the old supply line.
Secure the new water supply line to the threading on the bottom of the brass valve outlet on the underside of the sink. Tighten the nut at first by hand, then tighten it using an adjustable wrench.
Thread the other end of the new water supply line onto the water valve threading. Tighten at first by hand, then use an adjustable wrench to tighten further.
Turn on the water supply valve and inspect the connections for leaks.