The effect is achieved by taping the card to your thumb, as in the last picture; taping it from the nail to the card means that there will be a little bit of wobble, and will help to make the illusion more effective; if you like you can move your thumb a little bit, but not much, as it will begin to look fake.
Do not actively hide the fact that your thumb is behind the card, but try not to draw attention to it.
A few more things you could use this method for are floating a paper cup, (make it look like its floating away from you and follow it with your hands) and if you don't have any cards you could try a bankcard/note, or an empty matchbox.
I hope I made it clear how to do this, as this is my first Instructible.
Note: I did not make this effect, and I'm quite surprised not to find it on Instructibles! someone tell me if it's already is one. I don't think it's very well known, as a search for levitating card/object, does not turn up this trick.