The DHC-6 Twin Otter has two fuel tanks located in the belly of the fuselage, one forward (1235 lbs or 185 gal) and one aft (1341 lbs or 201 gal). There is a fuel fill port on the port side of the fuselage above each tank.
Refueling a plane is similar to refueling a car, except (a) planes can hold a lot more fuel than cars, (b) you rarely completely fill the tanks due to weight limitations, and (c) full service is fairly common.
However, with a very light load and a very long trip, you would completely fill the tanks to maximize range. That can mean 30+ minutes at the pump for a plane this size.
For self service, you taxi over to the self-serve pump, stop the engine(s), insert your credit card, attach the ground wire, insert nozzle, pump however much fuel you need, take the receipt, restart the engine(s), and taxi away.
For full service, typically you park on the ramp or at a terminal, call (on the radio) for a fuel truck, the driver does the fueling while you're parked, and you settle the bill before leaving.
Note: in less developed countries, you will likely have to pay cash (USD is accepted everywhere) before they will give you fuel, especially in large quantities. And a smuggler may not want bank records of their transaction anyway.
Normally, passengers will want to get out at fuel stops to stretch their legs, use the restrooms, get snacks, etc. But it wouldn't be unreasonable for passengers to remain aboard if the story has a reason for them to want to stay out of sight.