Upvote:2
The first thing to do is the get in touch with the nearest embassy or consulate and report the lost/stolen passport to the consular section. Whether by phone or in person, let them know the circumstances and when you plan to leave the country, so they know whether to get a limited validity emergency passport or a full validity passport.
In the case of theft, file a police report. If nothing else, it can assist in recouping costs through travel insurance, for example.
Get a new passport photo taken before visiting the embassy/consulate. Fill out the application and a statement about the lost/stolen passport. The latter is to ensure that your lost document is invalidated so that no one can use it (not even you, if you later find a lost document).
It usually requires some sort of identification, and not necessarily birth or naturalization documents: drivers license, picture id, photocopy of missing passport. If they are carrying none of these, try having them sent electronically.
Theyβll be expected to pay a fee, or make arrangements for someone elee to pay (e.g., via credit card). An emergency document can be issued fairly rapidly, usually within 24 hours, but the timing will depend on their circumstances and the consulate.