The practice of digging up graves to destroy vampires is thought to have begun in eastern Europe, spreading to France and England in the 1700s and to rural New England (which had a high incidence of death by tuberculosis), especially Rhode Island, in the late 1800s. As the article notes: “Often the vampire-hunters were not disappointed when they pried open the graves: many natural signs of decay, like bloating and bleeding from various orifices, looked like evidence of midnight feasts.” The means of “destroying” the vampire varied according to region, but included staking, beheading, and burning. (Fans of Bram Stoker's Dracula will remember that Van Helsing used the first two methods to destroy the undead Lucy so that she could rest in peace.)
What is particularly interesting about the Smithsonian magazine article is that it lists numerous historical figures believed by their contemporaries to be vampires, along with the circumstances of their deaths.
There is also a related article on the New England vampire scare that you might like to check out. It makes for very interesting reading.