I've been wanting to have a crack at this now I'm living somewhere hedge laying isn't very useful (there's another one for the list). How much more technical / skilled is it than just literally stacking stones - easy enough to do a decent job with a bit of practice after just watching a youtube video?
I had some instruction from a member of the dry stone walling association, who helped me pick up the knack, after watching me for a bit [and coming back to check one evening !] he then said that I had the eye/hand for it and left me to it ! I think because I would pick up a stone and place it far more aften than not, nor did I find the need to trim stone to fit.
Rebuilding can be much easier. It sounds easy written out ...
Take the wall remains down to the first layer of through stones that are stable - that might be ground level, so assuming the foundation layer is OK ...
When doing this destruction, spread the stones out so you can see what you have - keep the big toppers & throughs in one area and the tiny fillers in another, with the rest graded by size - heaviest nearer the line of the wall. Note, leave yourself plenty of room actually on both sides of the wall to work.
Start with larger stones first, try for the longer side lined up to the outside, and working on both sides. Avoid vertical gaps more than one row high. [ie one on two to cover the gap below] Keep the interior packed as you go with mostly irregular or softer material - unless building a hedge bank, try to keep soil out. Use the interior space to pack in wedges / chips to keep the outer face stable. After about every 18" put through stones in - their weight and size keep the faces together, as does the batter ie the lean back of the face as the wall narrows as it gets taller. If you are trying to keep sheep or goats confined, then don't let the throughs project out of the field face. To finish, the top layer should be covering the full width, and then you can put on coping stones.
There are additional things to do when walling up a slope / across a hollow / ending a wall by a gate / turning a sharp corner / adding in a tunnel for water or livestock to pass / including a style for humans.
If you are building a single skin boulder wall - good luck as that's a type I've not tried.
Also, to keep cattle confined, the wall needs to be very heavily built as they will lie against it - I need to talk to my neighbour to rebuild a patch of our joint wall as his beasts have been doing exactly that, which is pushing the wall off it's foundations.