Like most levitation tricks, the floating card is achieved with a piece of string. You should use a string that will be difficult for the audience to see, like a fishing line or a very thin strand of invisible thread designed for magic tricks. Attach the anchor end of the string before you begin the trick; you can hang it from the ceiling, or you can attach it to yourself using a headband or a piece of scotch tape. If you need to do this part of the trick while the audience is watching (as is the case if you are performing on the street), then attach the string behind your ear with a piece of scotch tape. Have the tape on your finger, and put it behind your ear as if you were scratching behind your ear or brushing your hair back while you're doing something else (such as showing both sides of the card) with your other hand.
Next choose an object to float. You can have a member of the audience pick a card from the deck, or you can ask a volunteer for a credit card or a dollar bill. After the audience has had a chance to look at the card, attach the string by taping it to the center of the card with a piece of scotch tape. This should be done quickly so the audience doesn't notice. You should have this piece of tape already attached to one finger so you can quickly press it on the card. You can use double-sided tape or even sticky wax to make it easier to transfer from your finger to the card. Again, do this with one hand while you are doing something else with your other hand (perhaps showing them that you have nothing hidden in that hand) to distract your audience.
Start the card spinning while it is still in your hands. The spinning not only makes the trick look better, it also ensures that the card is moving too fast for the audience to see the string attached to it. Spinning will also maintain tension on the string, which will help you better direct the object. Once it is spinning, you can let go of it and it will seem to float in the air. Use a finger to direct the string while cupping your hand above the card, and it will seem as though you are moving the card through the air without touching it. The trick is best if you switch back and forth between your hands, or even "toss" the card back and forth so the audience can see the card isn't tied to one hand. With practice, you can even pass the card around your entire body, which is usually used as the finale of this trick.