What do you do if you lose your passport abroad?
Report it, get a police report, and contact your country's nearest embassy or consulate — and the single thing that determines how painful this is turns out to be whether you kept a copy before you travelled.
The sequence:
Search properly first, including with the hotel, the last transport you used and any venue, since a great many are simply mislaid.
Report it lost or stolen to the local police, and obtain a written report with a reference. Many consulates require this, and travel insurance almost always does.
Cancel it with your own passport authority, which prevents misuse — and note that a cancelled passport cannot be used again even if you find it, which is why searching first matters.
Contact your embassy or consulate. They can issue an emergency travel document, which is typically valid for a specific journey to a specific destination rather than for general travel, and which may not be accepted for onward travel through some countries.
What you will generally need: the police report; proof of identity and nationality, which is where a copy of the lost passport, a driving licence or a birth certificate held remotely becomes valuable; passport photographs, which consulates frequently cannot take; details of your travel plans; and a fee, which is usually payable.
How long it takes. Frequently one to several working days, longer if the consulate is not in the city you are in or is closed for local holidays — which is why travel plans usually have to change, and why insurance covering additional accommodation matters.
Other consequences to handle: visas held in the lost passport are lost with it and may need reissuing by the relevant country; onward airlines will need the new document details; and hotel and rental bookings made against the old number may need updating.
What to do before travelling, which takes ten minutes and saves days: photograph the photo page and store it in an account you can reach from any device; keep a separate physical copy in different luggage; note your travel insurance emergency number; and record your consulate's details for the destination.