When booking a ticket in one location the entire route is considered a single operation (even if the carriers are different). Therefore, if one of the flights is late and disrupted the dock, then the responsibility for this lies with the airline that is obliged to deliver to the destination in any way. However, note that the flights with transfers are different categories.
A transfer flight with one airline, when the end points lie within the same customs space. For example, flying to Bali via Bangkok. In this case, the passenger and baggage is checked through to the destination the destination. Therefore, in the transit airport, you don't need to get Luggage and to register for the next flight. You only need to go from one plane to another. An important caveat: the airline for the entire route must be one and the same.
A flight with a transfer, when the end points of the route are in the same customs space. For example, a flight from Krasnoyarsk (Russia) Moscow (Russia) to USA. In this case, the passenger and baggage is checked only to the first destination (Moscow), then he gets the Luggage again, pass passport and customs control, registers itself with your next flight and re-take the Luggage. Some airlines still carry baggage from one flight to another flight without the participation of a passenger.
Flight with transfers involving multiple airlines. In this case, the passenger and baggage check-in with one company. At the transfer point, the passenger obtains their Luggage, recorded a flight of another company, again losing Luggage, pass through passport control. That is, the transplant is carried out independently. The airline provides no assistance. To find the check-in route, you may need knowledge of the English language, how to navigate in the airport will have the signs: Connecting fligts Transit passangers and others.
Change of plane takes place at the airport. So a transit visa to another country is not necessary. Only flights through countries such as the USA and Australia is prohibited without a transit visa. Keep in mind that transit visa allows you to stay in the country only 24 hours. For longer stays you need to get a regular visa.
Small airports have only one terminal. In the absence of queues at customs and passport control, transplanting is very fast. If the airport is large, it is definitely more terminals. Consider the time of movement, because often the journey between terminals can take 20-30 minutes.