Is it always cheaper to book multi-city?

Not always. Sometimes booking one long-haul 'base' flight and using budget regional carriers (like RyanAir or AirAsia) for the internal legs is cheaper, though it requires more effort to manage.

What if I miss a connection in a multi-city itinerary?

If all flights are on one ticket (a single PNR code), the airline is responsible for rebooking you. If you booked separate tickets, you are responsible for buying a new ticket.

How to book multi-city flights for backpacking

Use the 'Multi-city' search tool on flight aggregators like Google Flights or ITA Matrix to link your arrival and departure points into a single booking. This avoids the cost of one-way tickets and often keeps your itinerary under one airline alliance for easier baggage handling and rebooking.

Map your 'Open Jaw' route. Don't book a round-trip to the same city if you are traveling across a continent. Identify your 'fly-in' city and your 'fly-out' city, and search for these as a multi-city route rather than two separate one-ways.
Use ITA Matrix for precision. Go to matrix.itasoftware.com. Use the 'Multi-city' tab. It is more powerful than consumer sites and allows you to specify that you want to search 'all airports' in a city (e.g., LHR and LGW in London) to get the cheapest fare.
Check the 'Hidden City' risk. When booking multi-city, check if booking two separate one-way tickets on budget airlines is cheaper than a single multi-city ticket. Use a site like Skyscanner for the individual legs, but be aware that if you miss a flight, the subsequent ones are often canceled.
Keep the same alliance. Try to pick flights within the same airline alliance (Star Alliance, Oneworld, or SkyTeam). This ensures that if your first flight is delayed, the airline has a much higher obligation to get you onto the next connection.

Is it always cheaper to book multi-city?: Not always. Sometimes booking one long-haul 'base' flight and using budget regional carriers (like RyanAir or AirAsia) for the internal legs is cheaper, though it requires more effort to manage.
What if I miss a connection in a multi-city itinerary?: If all flights are on one ticket (a single PNR code), the airline is responsible for rebooking you. If you booked separate tickets, you are responsible for buying a new ticket.