What can I do to keep my shed (or house) free of spiders?
Spiders are predators, they go where the food is.  If spiders are attracted to your shed, it means prey insects are attracted to your shed.  Get rid of the prey.


Remove nearby vegetation and organic matter that provides food/shelter for bugs
Remove any standing water (bird baths, puddles, soil that soaks up moisture)
Remove light sources (bugs fly towards light)
Stain/paint exposed wood to make it less attractive to bugs
Fill gaps in the shed where bugs are getting inside to get out of the elements (caulk)
Regularly apply spray pesticides to the exterior surface of the shed to discourage insects from hanging around.  Also apply it to any crevices in the inside.
Look at more "natural" oils and plants that repel insects.