Business cards remain the most effective, conventional way of sharing contact details with another person.
They need not be corporate-style business cards form American Psycho. As with anything you issue, it should ideally reflect who you are and the nature of the work you carry out as an artist. Perhaps consider using an image on one side, hand-made aspects, or other ways they might reflect your practice. Lettering sets or printed labels enable you to add short-term information such as an upcoming show on the back of a standard business card.
Postcards offer much the same possibilities but with a larger, better resolution image on one side. Additionally, these could be sold as well as given away, if you can find someone to stock and sell them on your behalf (and you can afford to have them printed in good enough quality to begin with).