United States citizens traveling abroad face the risk of losing their passport or having it stolen at some point during your trip. Obviously, this is going to cause a major inconvenience, as you cannot travel back to the U.S. without your passport. If you find yourself in this situation, you should immediately contact the nearest U.S. Embassy or Consulate for further assistance. The American Citizens Unit at the Embassy is there to help you in any way possible.
Contact the nearest U.S. Embassy in the country where you are currently located. They will attempt to help you in any way possible, including providing you with information on obtaining a new passport.
Call a friend or family member in the U.S. and ask them to contact the Overseas Citizens Services in Washington D.C. Have them provide the OCS with as much information as possible about you so they can assist in locating your passport information to relay to the U.S. Embassy to have you cleared for re-entry into the U.S.
Apply for a new passport at the U.S. Embassy in the country in which you are located. You must provide the consular with a reasonable amount of proof that your identity is that of what you say it is. You must provide the consulate with your personal information -- it helps if you know your passport number -- and some form of identification.
Ask a friend or family member to speak with the consulate as a witness attesting to your identity, which is required when a passport is lost or stolen and you are applying for a new one. Once all of the necessary information is provided, you are issued a new passport and may return home.