How does air to air refueling work?

The Tanker aicraft has a crew position in the rear of the aircraft. The crewman lies on his stomach and looks out a window that faces aft and down. This crewman has joy-stick controls that literally flys the refueling boom. He can fly it up and down and left and right for a few degrees and he can extend the boom to make it longer. He also has controls to pump the fuel and transfer fuel from tanks inside the Tanker.

The aircraft that is receiving the fuel has a Universal In-flight Refueling Receptacle on the nose or on the top of the aircraft. This receptacle has a ramp that guides the Boom into the hole. Once connected, it snaps into position and that gives the Refueler a "Go" light. The nozzle can flex a few degrees to allow for pitch and yaw caused by air turbulence.

I've flown on a refueling mission on a KC-135 that refueld an FB-111B. You could look down and see the insignia on the Fighter pilot's shoulders.

During the Viet Nam War, there was an emergency with an aircraft that could not refuel with an USAF KC-135. So they got a Navy jet to transfer the fuel. This was the first time that 3 aircraft performed a simultaneous in-flight refueling.