How to Care for an American Staffordshire Terrier. Part of the series: Medium & Large Dog Breed Care. Proper care for an American Staffordshire terrier includes utilizing the breed’s high energy, enthusiasm and intelligence with proper obedience training and exercise. Learn about how the American Staffordshire terrier is similar to a pit bull, but with more companion instincts, with information from a certified dog trainer in this free video on dog care and obedience.