The rules of wizard chess are exactly the same as muggle chess. However, the pieces are animate and commanded by the player like troops on a battlefield (PS12).
Ron had a wizard chess set which he inherited from his grandfather. Unlike many of his hand-me-downs, the second-hand chess set was advantageous as the pieces trusted him (PS12).
When Harry played with Seamus Finnigan's chess men, they did not trust his judgement and offered him advice (PS12).
Harry won a wizard chess set in a cracker at his first Christmas dinner at Hogwarts (PS12).
Hermione loses at wizard chess, which Harry and Ron believe to be a good experience for her (PS13).
Professor McGonagall transfigured a life-size wizard chess set to serve as one of the defences for the Philosopher's Stone (PS16).