How did dumbledore destroy Lord Voldemorts ring?

In the Harry Potter series, Dumbledore did not destroy Lord Voldemort's ring. Dumbledore was killed in the sixth book ("Harry Potter and the Half-Blood Prince") by Severus Snape, who was acting under Voldemort's orders. It was Harry Potter himself who ultimately destroyed the ring in the seventh book ("Harry Potter and the Deathly Hallows"). Harry used the Sword of Gryffindor, a powerful sword made from goblin steel, to destroy the ring because it was one of the few things that could damage a Horcrux (an object that contains a fragment of Voldemort's soul).