The dealer deals all of the cards to the players (some players may have 1 more card than others, this is ok). Players look at their cards and discard any pairs they have (ie, 2 Kings, 2 Sevens, etc).
Beginning with the dealer, each player takes turns offering his hand facedown to the person on his left. That person selects a card and adds it to his or her hand. This player then sees if the selected card makes a pair with their original card. If so the pair is discarded. The player who just took a card then offers his or her hand to the person to their left and so on.
The object of the game is to continue to take cards, discarding pairs, until you are left with no cards. The player left with the 1 odd queen (that has no matching queen) is stuck with the "Old Maid" and loses.
This game most likely originated in China or India.