What happens if a chess player wants to promote his pawn to a queen (after reaching the eighth rank), but his queen is still on the chessboard?

Since the queen is the most powerful piece, the vast majority of promotions in practical play are to a queen. If the queen is not available, the official rules are that the player should stop the game clock and summon the arbiter for the correct piece. In casual play, an upside-down rook may be used to designate a queen. Some finer sets do include an extra queen of each color.