This is the trick
Step 1: The Set-up
Introduce yourself, and show your audience that you are using a full, regulation deck that has been shuffled.
Step 2: "Pick A Card"
As they are looking at it, cut the deck in half, then into fourths of relatively equal size, and position them in a line.
Step 3: Lose the Card
Ask the person that drew the card to place it ontop of any one of the four piles. It does not matter what pile they place it on, just keep an eye on that pile. Once the card has been placed, grab any two of the three piles (that dont have that card ontop of it) and shuffle the two together, bridge style. Then set the combined stack to the side. Then grab the two remaining piles and shuffle them together, making sure that the chosen card stays ontop of the combined stack. In this case, the chosen card is the Two of Clubs. (see picture two as a reference)
A little trick that I do is keep the thumb of the hand holding the unimportant pile as slack as possible, and the thumb of the hand holding the important pile as taught agaisnt the edge of the cards as possible, obviously not so much as it is noticeable. Once you have two stacks remaining, grab the other with your free hand and shuffle the two stacks back together, again making sure the chosen card lands ontop of the newly formed deck.
Step 4: Re-shuffle
Now repeat step 3, making sure you keep the chosen card ontop of all shuffled stacks, trying to be quick about shuffling, and remaining as descrete as possible about your dirty little shuffling technique. Once your finishing the shuffling process, sometimes I find it good to mock your shuffling and suggest inconspicuously, and slightly cynical that you are lucky shuffling isn't a crucual part in this trick. Make sure its after you shuffle, or that might get them to look closer at how exactly you are shuffling the cards.
One final tip about the shuffling technique:
Try and switch hands with the stack that has the card ontop of it, just so it doesn't look like one side of the shuffle is always landing ontop of the other.
Step 5: Now for the Magic
Tell them that it would do no good to go searching for it in the deck, so your best option is to move it to the top (or something along those lines).
So snap, wave your hand, tap the top of the deck, or say a magic word (whatever your magical gesture preference), and claim that the card is now ontop of the deck.
Step 6: Pulling the Card(s)
Then, as you finish saying your piece about how the audience doesn't trust you, quickly grip the top two cards together and whip them out and around, trying to keep them as lined up as possible with each other so that it looks like one card. (picture 3 shows the incorrect way to hold the two cards; picture 4 shows the correct way to keep the two cards flush) Laugh and tell them you have successfully found the card that they chose.
Step 7: The Flip
Here is how to do the flip in detail (use pictures as a guide):
Grab the two cards as shown in the first picture. Only about an eighth of an inch of your middle finger and thumb should be above the cards. Gently switch the pressure applied by your fingers down on the bottom card, which will make the top card slightly loose. To do this, subtly roll your fingers in and under so they sort of taper down and in on the bottom card and up and out on the top card. This way, when you bend the card upward, it should raise VERY SLIGHTLY off the bottom card (picture two is overly dramaticized to show you how the two cards seperate in the bend). Then bend it a couple times, which sort of slowly raises the top card loose. Do this until the top card flips off. If done correctly, it will flip about a half a foot to a foot away, and you should still be holding the bottom card, which is the original card that was chosen.
Pictures 3, 4, and 5 show the three stages of the card flip.
Step 8: GLOAT!
THERE YOU ARE DONE!
Oh and due to the difficulty of the card flip, the next step has several alternatives that work just as well.
Step 9: Alternatives to 'The Flip'
Grip the two cards flush with the thumb on one side, and the middle and ring finger on the other. Apply force with your thumb in and up so that the edge of the card "pops" off of your ring and middle finger. This quickly collapses the bottom card flat against the right and middle finger, with the thumb holding it in place, while simultaneously popping the top card off. View pictures one and two to understand better.
Grasp the bottom of the cards between the thumb and the index finger, slightly firm, but slightly loose. Play around with the method to get a feel for how tight or loose a grip you need. But simply slap the top part of the top card, and it should fly off, leaving the bottom card remaining within your grip. Pictures three through five illustrate this.
Grip the cards as shown in picture seven, against your first three fingers, held in place by your thumb. Then, throw the cards downward, moving your thumb away and keeping the cards in place by slightly squeezing the sides between your index and ring finger. The centripital force should keep the back card against your fingers and force the front card to slide off. After the front card has plummetted to the ground, move your thumb back over infront of the card to keep it from falling as your arm stops. Refer to pictures six through eight to see this process
This video should help