Begin by chalking up the edge of any card; we'll say the 10 of Diamonds. Place it back in the deck. Even though it is marked, nobody will really look for that.
Hand the sealed envelope with your prediction inside, "10 of Diamonds," to a second spectator and have the first spectator shuffle the deck.
Make sure the chalked card is close to the center, so if it isn't, you should shuffle it there. Cut the deck into two piles.
Tell the spectator, on second thought, HE should cut the deck. After he cuts, tell him to pick a pile. If he chooses the marked card pile, you keep it. If not, tell him you'll discard the other pile. Now you're left with just the marked card pile.
Ask him to deal the cards, one to you, one to him, to form two piles. The marked card will be at the bottom of your pile. Make sure to stop him after dealing seven cards to you, however, then discard the rest.
Tell him to deal your pile the same way, so he gets three and you get four. The marked card is now atop your pile.
Once again, have him discard his pile. Now deal the remaining four cards, two to each. Run through the pile-choosing method again (If he chooses the marked card pile, great, you'll keep it. If not, you will discard the other).
With just two cards left, repeat the previous two steps to end up with the marked card and then have the second spectator reveal the sealed envelope.