Regular toothpaste works great to remove old tarnish from silver. Make sure to not use gel toothpaste. Regular toothpaste has just enough abrasiveness to cut through the toughest spots, but is gentle enough to not damage the surface. Always test your toothpaste in an inconspicuous spot, as their are many different brands out there. To clean, just use a clean microfiber cloth and work in circular patterns. Toothpaste is much safer than the commercial polishes and cleaners which often contain petroleum-based ingredients and other potentially dangerous chemicals.