"I'm curious how you would even begin to guess at his age."
A lot of experience looking at deer, which I believe the gentleman that posted this does have.
" Without having a LOT of expertise and his jawbone in your hand you couldn't even start."
Yes you can. With some practice just about anyone can start "aging" deer on the hoof. No different than a rancher eyeballing a calf at the sale. I am not saying that you can tell if the deer is 47 months old, but you can tell if he is in a specific age class. For example on the hoof you should be able to tell if a buck is 0-2 years, 2-5 years, 5-7 years, and 7+ years in age. This can actually aid you with conservation and management.
"And the only way you could be very accurate would be with a section of his tooth under a microscope. Both will be difficult until he is dead."
Actually tooth cross sections in deer are still under debate as to the accuracy of their findings so they are not exact either. The best tool for aging deer is still collected trend data within a specific set region on dead individuals. People tend not to like this because it is labor intensive data recovery and it only becomes more and more accurate over time for a specific population. Every one still wants the silver bullet for aging animals but unfortunately it does not exist.