Step #1. Find out where the U.S. Embassy is located in the country where you are currently vacationing. A quick way to find out the locations of the various U.S. Embassies around the world is by visiting travel.state.gov.
Step #2. As soon as you figure out the location of the U.S. Embassy, you need to make an emergency appointment to get a replacement U.S. passport. Most U.S. Embassies don't allow walk-in appointments.
Step #3. In order to expedite your emergency appointment, be prepared to bring with you or fill out the following documents; a completed DS-64 which is the form for the lost/stolen passport and a completed DS-11 which is the form for the new U.S. passport. If you have access to the internet, you can download these forms and fill them out before your appointment. In regards to supporting documents, you will need to have a valid U.S. Birth Certificate or a U.S. Naturalization Certificate and a form of identification i.e. driver's license, state ID, US Government ID or a Military ID.
Step #4. Most American travelers don't travel with their birth certificates so it is best that you make sure your birth certificate is somewhere close where a family member or friend can locate it and Fed-Ex it to you for overnight delivery.
Step #5. After you have submitted all of your documentation, you will need to pay the appropriate fee in order to obtain the limited U.S. passport. The fees for the limited US passport are as follows:
U.S. Passport New - $135
U.S. Passport Renewal - $110
U.S. Minor Passport - $105
Add Visa Pages - $85
Step #6. Depending on the schedule at the U.S. Embassy, you may receive your limited validity U.S. passport on the same day or within one business day. This passport is only good for one year and will need to be renewed and replaced with a traditional 10-year passport once you have returned back to the United States.
Most U.S. Embassies takes all major credit cards, cash, traveler's checks, money orders and banker's drafts, however no personal checks are allowed.