It's going to depend somewhat on the airplane type.
In general, the tug should be lined up with the aircraft when pushback is complete. The headset operator should call for "brakes set" and receive a compliant "brakes are set." It is usually necessary for the tug to set gear into neutral and let off the brakes to "unload" the weight of the aircraft pushing on the bar (hard to impossible to pull the pin out).
At this point the headset guy may pull the pin (if on some airplanes the NWS was not in bypass, and the tug is misaligned with the aircraft, if the pin puller manages to pull the pin and is standing on the wrong side of the bar...ouch!).
After that you disconnect the bar from the aircraft, pull it out, reconnect to the tug, and have him drive off. Then disengage NWS ground bypass, show the pin if necessary, and carry on.
How it works in real life varies widely.