Assuming it's a permanent structure, if the shed is for the exclusive use of the paying renter, then it's classified as a rental property asset and depreciated over 27.5 years If the shed is not indicated on your property tax bill (meaning that no permits were required to build it on your property) then it's just a storage shed and can be expensed as such, provided it's for the use of the renter.
If the shed is for your personal use (such as storing rental equipment or supplies) then you have nothing to claim on the SCH E or elsewhere on your personal tax return.
