Soak a paper towel in white vinegar and wipe over the faucet. Continue until all of the residue is removed.
Run a clean paper towel under water and rub over the faucet to remove the vinegar residue.
Dry the faucet with a clean paper towel. Also dry the faucet each time you notice water splashing onto the faucet.
Twist off the faucet head, washer and similar parts that still have hard water buildup, and soak these in a small bowl of vinegar for about one hour, making sure all parts are submerged.
Scrub the parts with an old toothbrush. Rinse them with warm water and dry with a clean rag.