The game is called Teuchre, and involves playing as your opponent's partner twice (i.e. partnered on two sets of hands, with four hands playing the game). Your goal for one set is to have the set win, and for the other set is to make that set lose.
More detailed explanation later, but for now, just know this:
if you play it, I think you will love it. Unless you hate cards or trying to win and lose at the same time.