Garth,
There are two styles of nose gear doors on the B-24, inward and outward opening. Like all things Liberator, it is a little confusing to figure out which manufacturer did the doors which way...... If memory serves, Consolidated originally designed the airplane with inward opening doors, then Ford came up with the outward retracting setup, then Consolidated adopted the same arrangement in later "J" production.
Here is Consolidated-built AM927 with her original short nose:

And with the RY-3 nose that was installed late in the War--it still has this nose door arrangement today:
Witchcraft is a late production Fort Worth-built airplane and also has the outward acting doors.
StrawberryBitch is a Consolidated San Diego "D" and has inward acting doors.
Regardless of whether the doors open inward or outward, they work in the same way as skymster02 stated--the doors are driven by the landing gear strut assembly.
If you aren't confused by all the redesigns and changes, just start studying the B-24 in detail. There were LOTS of changes during the production of all those Libs.
Scott