One of my friends said that you had to sleep with them under your pillow for a week before they would actually "belong" to you.

Or, you can just stick them in your underwear. :-)

No. Although there are many personal traditions that go along with tarot card reading that may be very beneficial to particular people.

The real answer is: If you feel it helps you establish a better connection with your cards, then why not? But it's certainly not a requirement for a successful reading.

The proof of this, is that online cards (like http://www.ifate.com ) can often yield incredibly accurate readings, and clearly one can't sleep on those...