Brumation is typically somewhat in fall, winter (to avoid times of lower temperatures, less daylight), but can vary from dragon to dragon.
My dragon starts brumation in early fall (which is right now for us, as we live on the Southern hemisphere).
During brumation, I just leave my dragon alone. I also do not "put" him into brumation - he does it on his own. Generally, I take my dragon out of his enclosure when he's active and wants out; regardless whether it's brumation or not, I don't grab my dragon and take him out, but only take him out if he actively approaches me when I reach in. (Emergencies would be a different situation, of course.)
My dragon is currently brumating.