looks to me that the square ended buckle would go on the right side, as the billet on the saddle on that side does not usually require the same sort of 'doing up' as the latigo (the proper name for the billet on a western saddle) on the left side, and the right side does not get adjusted once you have it set to the proper hole on the billet, and the cinch is even with the centre of it at the centre of the horse's underside.
The left side latigo will be run through the round ring of the girth (cinch), going from the side of the ring that is facing the horse, then back up to the ring on the saddle, then back down through the cinch ring one more time then back up to the saddle, then looped around horizontally once (front of saddle to back) then up through the ring again and back down on the inside of the horizontal loop you created. Some left hand latigos on western saddles have holes for the buckle 'pin' on the cinch to go through, some don't. I have had to remove the 'pin' from the left side of a western cinch before as my saddle did not have holes in the left side latigo.
Hope that helped and was not too confusing!
Last edited by EdmontonHorseGal; 06-07-2013 at 02:44 PM.