It varies from a few day to never. If you do not get a refund in 7 business days file a dispute with your credit card.
http://www.united.com/page/article/0,6722,1511,00.html
Provide prompt ticket refunds
United's Commitment:
We will issue refunds for eligible tickets within seven business days for credit card purchases and within 20 business days for cash purchases in any instance in which refunds are appropriate.