You will be met at the air-bridge, escorted to through any visa, quarantine, transit, security, immigration, baggage, or customs procedures; then you will be led to the next flight’s check in area, or to flight transfer desk, or to your airline lounge, or to the boarding gate.
If a change of terminal is required the greeter will normally accompany you between terminals. If requested and the distance between terminals is great, an “inter-terminal transfer” in a private vehicle can be organized for an additional cost. Otherwise the airport shuttle or transfer system will be used to move between terminals.
In some airports “international to international” connection may not be permitted solely within the transit area. Or maybe a low cost “point to point” carrier’s flight might be involved (which does not support transfers), or possibly different tickets might have been issued and/or bags not labelled through to the final destination (not “interlined”). In these cases the airport layout, regulations and agreements may require you to pass through immigration, collect your bags and check in again. Each request will be evaluated case by case and a solution will be will be suggested and quoted at the time of booking.