Gather as many specifics about the emergency situation and your impending travel plans. Having as much information as possible before contacting the U.S. Department of State will facilitate the process. Try to decide how you will be traveling out of the country. For example, a general idea of which airports you may leave from and travel to is useful information.
Call the National Passport Information Center immediately. The telephone number is 1-877-4-USA-PPT (1-877-487-2778). Representatives are available from Monday through Friday from 8 a.m. to 10 p.m. EST, excluding federal holidays. Passport information is available 24 hours a day, seven days a week.
Dial 0 to immediately speak with a passport representative during regular business hours. If you are calling outside of business hours, listen to the voice prompts and carefully follow the instructions. Eventually, there will be an option to speak to a representative who is available for travel emergencies.
Relay your situation to the National Passport Information Center agent on the line. Be as specific as possible. Follow the agent's instructions carefully. Depending on your situation, you may be asked to travel to a Regional Passport Agency to speak to a representative in person. In some cases, emergency documentation can be organized entirely over the phone and sent in the mail. There are no hard rules and procedures for obtaining the passport at this point. It is in the hands of the agents.
Contact your local U.S. embassy for instructions if you are living or traveling outside of the country and need a passport immediately. You can find the contact details to the nearest U.S. embassy using the link in the Resources section. The ambassador or the ambassador's subordinates are generally able to issue emergency travel documents for U.S. citizens stranded abroad. Since you presented a passport to travel outside of the U.S. in the first place, this situation should only be when your passport is lost or stolen while you are in a foreign country.