As Michael Caine's character states at the start and end of Christopher Nolan's 2006 movie "The Prestige," a trick consists of three acts: the Pledge, the Turn and the Prestige. For the flying credit card trick, you begin with an ordinary credit card. You can also replace this with any card. This part of the trick is important. The audience must realize that you have done the extraordinary with something quite ordinary. This can be done by either borrowing a card from your audience or showing them the one you have.
Taking a normal credit card between your index and middle fingers, move your arm as if you were going to toss it straight up into the air. Keep the back of your hand to the audience. Move your arm up and down three times. On returning your arm to the lower position, slip the card into the palm of your hand by bending your fingers quickly toward your lower palm. Hold the card against your palm with your thumb as your fingers come back into position to toss the card back up into the air. Follow this invisible card into the air. The card has disappeared. Now you must make it reappear before the owner's fist makes your nose disappear.
It is not amazing to make something simply disappear. That's called stealing. You must be able to conjure it back. Act as if the card is landing back in your hand. Then follow it with your eyes as you "catch it." As the imaginary card comes down, reach back with your index and middle fingers, grip the card, and pull it out by releasing your thumb's hold on the card. Everything you do here is to "help" your audience see the card come down. So react with your body as if you were tossed a book. Try it. Have some one toss you the phone book and notice your natural reaction in front of a mirror. Practice before attempting this trick.