Holding a deck of cards face down in your left hand, take a small bunch of cards with your right. Turn the cards in your right hand face up, and put them on top of the cards in your left. Square up the deck. Grab all of the face up cards and a bunch more from your left hand. Take this new stack of cards, turn it over and place it back on those in your left hand. Continue this process until you've exhausted the entire deck. The cards now appear to be hopelessly mixed, face up and face down.
The cards are really just divided into two halves, facing each other. (But don't tell the spectators this.) Find the place where the two piles come together, and separate them. Put the piles on the table and give them one quick riffle shuffle. (The kind where you flip the edges of the cards so they interlace.) Now spread the cards out, to show they have been magically restored to order!