I was pretty clueless until mine seized up on the stud!!
So off with it's head - has to come off to get that bugger out of there. The spring in there is designed to hold the tension, so you simply loosen the nut while holding the stud to make sure it doesn't turn. When loose the mechanism will put all of its force into tightening the chain, kinda like a belt tensioner on a modern automobile serpentine system. Depending on wear, you may "see" it move a lot, probably not at all. Then just hold the stud while tightening the nut. I put anti seize on mine given what happened.
These are a known weak link on these bikes, but IMO, just because it's so easy to jack up/ignore during regular maintenance. I've yet to hear anyone wax poetic on how they religiously adjust theirs.
Queue for those who have to chime in.
Also helps to have the dog watch.