First you need an account on PostCrossings http://www.postcrossing.com.
This is free, but you will need an email account (not unlike this fine site).
As a personal note, I suggest you mention your hobbies and the kinds of cards you would like to receive on your profile. This helps people sending you a card to select a card that best fits you interests. I also suggest a face picture, but understand that some people feel uncomfortable with that.