the most commonly referenced delivery maneuver seems to be the Mauriceau‐Smellie‐Veit maneuver:
the basics to get to that point seem to be:
–wait till you see the popliteal fossa, then sweep/deliver the leg
–wait till you see the scapula border, then rotate gently and sweep/deliver the arms
–wait till you see the nape of the neck, then deliver with the MSV maneuver
quick snapshot visual aid:
quick video visual aid (relatively short, with decent audio):
There you go. Add it to the emergency toolbox.
References: guidelines, photo visual, video visual