I've spent most of my short life around wooden antiques, and although I am by no means an expert I can offer you one piece of advice for how to take care of the board:
Keep water well away from it, and that goes for all water-based liquids. Not only will it completely destroy any finish that has been applied to the wood, if the board is inlaid (as it appears in the photo) then the water will cause the woods to crack and swell at different rates to the point where pieces actually start falling off. If you should spill a cup of tea or something on the board get to it IMMEDIATELY.
Sorry if that sounds a bit forceful, but I've seen so many absolutely beautiful antiques ruined in this way (I've seen a lot - my father repairs antiques professionally).
EDIT: The pieces should be more durable as it looks like they're varnished. Looks like a lovely set, though.
So I just inherited my Grandfather Les's chess set. He was born in 1890, so it's probably an early 20c chess set. Love the board (and I'd love any recommendations on cleaning and care) as well as the genuinely goofy looking facial expressions in the kinghts.
The newspaper clippings are a sheaf of chess puzzels from the Christian Science Monitor.