He should play as much as possible. This will help him get the feel for the decision making that is such a big part of the game.
Also -- and this will sound old school, but -- I would get him a few balls that you're OK with getting destroyed. Find him a brick wall somewhere, where no one will object, then have him go to that wall every day and throw repeatedly against the wall. If he's been playing, he should be able to handle 100 throws easily. He should advance to 200 soon enough. In my youth, I would often do this repeatedly over summer days and weekends, and I got to where I would just see how many throws I could get in. I think my personal best was 2,000 in one day. I used to do this against the side of our house. Other times, when my mom couldn't stand the constant pounding noise, I'd ride my bike up to the local school (when it wasn't in session). The important thing is that there be no doors or windows in the area where you're throwing!
To be clear, we're talking about gripping the ball, throwing it, and fielding the rebounds. We're not talking about pitching or max effort throwing.
You will find that he quickly gains the ability to grab and throw without having to stop to think about it, and that his hands gain dexterity very quickly. He'll build calluses where he needs calluses. He can also advance to working on the fielding position (crouch with glove forward), shuffle step, etc.
I know of no better way to get tons of reps regularly and in a short period of time.
I'll also say, nobody does this sort of thing any more. If your son does, by springtime he will likely have surpassed most if not all of his JV teammates.