Mix a small amount of vinegar and water in a 50-50 solution in a spray bottle. Spray the solution directly onto the faucet, let sit for a minute or so, then wipe the vinegar and cloudiness away with a damp sponge.
Remove a stubborn cloudy buildup around the spout of the faucet by pouring some vinegar into a sandwich bag, filling the bag 1/3 to 1/2 full. Place the bag over the spout, wrap the bag opening tightly around the faucet and secure it with a rubber band. Remove the bag after several hours, then wipe the faucet and spout with a sponge. Use a nail brush to clean buildup in any grooves near the spout.
Mix baking soda and just enough vinegar to moisten it thoroughly in a shallow bowl. Apply the resulting paste with a damp sponge or with your hand onto stubborn cloudy areas on the faucet. Allow it to sit for an hour or so before rinsing and wiping with a damp sponge. Scrub with a nail brush, if necessary.
Rub a squeezed lemon half over the chrome faucet to remove cloudiness on the metal. Wipe down with a damp sponge, then dry with a soft cloth. The acid in the lemon juice works in much the same way as vinegar to remove mineral or hard water deposits.