Report your passport lost or stolen. This can be done by calling 1-877-487-2778, toll free. Another option is to print for DS-64: Statement Regarding Lost or Stolen Passport and submitting it to the following address:
U.S. Department of State
Passport Services
Consular Lost/Stolen Passport Section
1111 19th Street, NW, Suite 500
Washington, DC 20036
The form must be completed in black ink and signed in front of a notary (Reference 1). The form is necessary to report a lost passport, and will subsequently invalidate that passport. Even if a lost passport is later found, it cannot be validated once reported missing. (Reference 1)
Print the necessary forms. These forms are the DS-64 mentioned above and the DS-11: Application for a U.S. Passport. The loss of an old passport does require applying for a new one. However, the time needed to process is not as long as for an original passport. Be sure to print and complete both forms in black ink, saving the signature for when a notary is present. Forms should be completed legibly and in block letters, as well.
Take the completed forms to an appropriate location. One proper location is the U.S. consulate office if you are abroad while the passport is lost. If abroad and a replacement is required immediately, find the nearest embassy and make an appointment. (Resource 1) If still in the continental United States, locations should be a bit more accessible. Passport agencies are acceptable locations for submitting the replacement forms. Located in major cities, each state has an agency. (Resource 2) However, if a passport agency is not located nearby, then local acceptance facilities are available. Searchable by location, the "Passport Acceptance Facility Search Page" allows a narrow search of facility locations. (Reference 3)