If your passport is lost or stolen while abroad, you must replace it before returning to the U.S.
You must contact the closest U.S. Embassy or Consulate. (list)
Travelers need at least six (6) items to apply for a replacement passport, specifically:
A passport photo (one photo is required, and the agency recommends getting it in advance to speed up the process)
Identification (i.e., a driver's license, an expired passport, etc.)
Evidence of U.S. citizenship (such as a birth certificate or a photocopy of your missing passport)
Travel itinerary (like airline or train tickets)
Police report (if applicable)
Completed DS-11 application (may also be completed at the time of application)
Completed DS-64 statement form describing the circumstances. (may also be completed at the time of application)