According the official site:
If your bags do not arrive at your destination, report this to the United baggage agents in the claim area/office before you leave the airport. It is important to do so as soon as possible so we may obtain information pertinent to locating your luggage. Please note that all lost, damaged or delayed property must be reported to United within 24 hours.
In addition, a written claim giving full description and value of the missing property must be submitted to United within 45 days of the occurrence. If your bag was misplaced, we will make every reasonable effort to return your checked baggage within 24 hours in the United States.
I think you are interested in this section:
If your bag has been located and returned to you, and you still wish to request reimbursement of related expenses, send your request in writing, within 45 days of the occurrence, to the following address. Please include a copy of your ticket receipt, any baggage claim checks, a copy of your delayed baggage report, and any itemized purchase receipts pertinent to your claim.
Central Baggage Services - HDQLZ
P.O. Box 66140
Chicago, IL 60666-0140