Whenever you store your snowboard and do not intend to use it the next day again (unless you really like your board), then do the following
For longer storage, usually summer storage, do the same as above and
Wax the base, but do not scrape off excess wax. It adds some protection while storing.
Store in dry and cool place (with higher importance on dry).
Loosen the screws of the bindings.
Storage position is somewhat debatable. If you have the space, horizontally is certainly a good idea, but I always store them upright. Just take care that it wont get knocked over.
The loosening of the binding is kind of optional, I never do it but my board is second hand, so I do not care too much. The waxing on the other hand is absolutely essential for the base and it is fast and easy to do at home, the necessary materials are not expensive either.
The same (except loosing of binding screws) applies to skis as well.