Or if you're male,
doctors would insert the bag into the rectum, pass it through an incision into the abdominal cavity, use laparoscopic instruments to put the kidney into the bag and seal it, and then pull it out through the anus via the string. Then they'd open the bag and transplant the kidney into the recipient.
It's not without it's detractors however as Becca, a Spokanicity member, commented, "Good god! Pooing a kidney? That can't be fun."