Repairing a river stone mason wall

My son is planning to repair a 3' wall made of stone masonry for his Eagle project. We have never done this before. We figure we need mortar and some river rock, but that's about the extent of our knowledge. Does anyone have any thougths or suggestions about how to fix this thing (pictures linked below)?

River rock wall Eagle Project

 

Welcome to the forums, and congratulations to the son for his achievement!! Basically, you won't be able to find stone that will fit the pocks in the wall exactly, so the cement that originally held the rocks will need to be chiseled or ground off. Lotta work. Do it even in the smaller areas so you will have a smooth place to put the new rock. Find rock, of course. It is cheaper to use concrete and sand, mixing your own 3:1, but you can use bagged mortar/sand mix. Don't mix it too loose. You want it to clump in your hands but fall apart if you throw it in the air and let it land back on your hand.
An underlayment of wire lath attached with cap nails would be really good. Once you have the underlayment on, then you will put a scratch coat on the lath, covering it somewhat. Then butter the back of each stone and apply it to the scratch coat in a twisting motion to seat it well. Continue this until you have all the rock on. You can then mix mortar a little wetter, not much, to strike in between the stones. This will give a really strong bond throughout.
Now, with all this said, your stone work will outlast the remainder of the wall, so be prepared, years down the road for the other stone to loosen and fall. Pass your experience on to another for their project. Write it all down, with pictures as you go. It will be invaluable.
Good luck with the project.