And from ARRL:
QSL cards are similar to postcards. Hams exchange QSLs to confirm their radio contacts with other stations. Making a contact with the ISS is an exhilarating experience. But waiting for that coveted QSL card requires patience.
Send your QSL cards or report including date, time in UTC, frequency and mode (voice, packet or sstv) to one of the following addresses. If you wish to receive a card, you must include a large, self-addressed, stamped envelope with proper postage. DO NOT send cash or IRC coupons.
For the USA:
Bruce Hunter, W6WW
ARISS USA QSL Manager
13436 Lakota Road
Apple Valley CA 92308
Find instructions for QSL cards for other countries on the ARISS.org website.