How To: Do a simple but cool magic trick with a deck of cards

This video from Do as I do presents a simple card trick.
Cut the deck in half.
Give a half of deck to the spectator.
Ask to pick any card he likes, in this tutorial - Ace of diamonds.
Place the card face down in front of him.
Do the same thing with your half of deck, but while spectator is picking his card, turn over the bottom card of your deck, in this example - Six of hearts. Then pick a random card, in this example - King of clubs, and place it face down just like spectator did.
Place your half deck with turned over Six of hearts on top near your picked card.
This manipulation is easy to do because spectator is picking his card too and is distracted.
Then both write your cards on a piece of paper. He writes Ace of diamonds you write Six of hearts.
Then ask the spectator to place his card in the middle of your pack, trying not to spread it and show it's upside down.
Then you slide your card (King of clubs) in spectator's half deck.
Then ask the spectator to cut their pile in half, and flip it upside down, put it on the top of your pile and flip the rest of spectator's cards upside down and put it on the bottom of your pile.
Then hand the cards to the spectator, having him holding the cards in his hand, wave your hand over the cards, do any magical gestures you do, and then show that all the cards are face up except the selected by you and spectator. Voila!