First, download the TSA Claims Management Branch Tort Claim Package (pdf form) and carefully ... receipt of the damaged or lost luggage, your airline ticket, baggage tags, repair or replacement ...
If your bags don't arrive at baggage claim ... has been lost - If your luggage is missing for more than 21 days, airlines declare it lost. At this point, you can file a claim for reimbursement.
Don't leave the airport without a claim number. Typically, your lost luggage is in the baggage-claim area. Maybe someone else saw your bag, thought it looked like theirs, and took it by accident.