It's one of those things that somewhat simple overall, but a real bear to explain with anything approaching brevity. And that's without getting into all the interesting tactical/practical side discussions.
It may be best if you download the Maneuvering Board Manual from here. You can just download Chapter 6 if you like.
http://msi.nga.mil/NGAPortal/MSI.por...2&pubCode=0008
Example 25 in Chapter 6 lays out the procedure for COURSE, SPEED, AND POSITION DERIVED FROM BEARINGS ONLY. If you have questions I can follow up.