Keeping the mouthpiece of a musical instrument clean is a good idea, especially if you aren't the first person to use it. You may be borrowing a friend's instrument or buying a used one, but whatever the circumstances, disinfecting the mouthpiece will help protect you and your mouth from whatever bacteria could be squirming on the surface. Even if you're the only person playing the instrument in question, giving the mouthpiece a good cleaning every now and then is highly recommended.
Spray the mouthpiece with a specially formulated mouthpiece cleaning spray. Some companies make special sprays that are designed for sanitizing musical instrument mouthpieces, but their effectiveness varies.
Wipe the mouthpiece down with an alcoholic medicated wipe. This kills bacteria. Rinse it off afterward to avoid as much aftertaste as you can.
Cleanse the mouthpiece with alcohol. Douse a clean cloth with alcohol--rubbing alcohol or even a flavored alcoholic mouthwash will do. Rub the mouthpiece down thoroughly.
Soak the mouthpiece in a tall glass of hot water and soap or non-toxic detergent . Gently scrub the mouthpiece with a soft brush, and rinse it thoroughly before returning it to your instrument.