I'm no expert at this but I'd probably just bring them indoors and leave them somewhere mild but not too hot. Scrape the bark off to avoid bringing any bugs into the house.
Weigh them once a month or so: after a month with no change in weight they're probably ready.
I suspect water will escape from the cut ends more easily than through the sides. Lots of tiny xylem pipes run through the branch from the trunk towards the leaves. Hence it might help to place the pieces on their sides and leave the ends exposed.
Fresh cuts across the big knots might help to open up the ends of more little pipes which lead into the heart of the wood. It sort of makes sense in theory but I don't really know for sure.