How should a dslr camera, lens, and batteries be stored if they aren't going to be used for weeks-- if not months? Is it dependent on manufacturer (Nikon, Canon, etc)?
Is there any risk of damage if it's stored away for an extended period of time?
You can either store the camera with the lens attached, or separate with lens and camera covers attached.
How to store batteries depends on what kind you are using. Rechargable batteries should be safe to keep in the camera, chemical batteries should definitely be removed as the can leak acid after a long period of storage. The only reason to keep the batteries in the camera would be to not lose the settings (e.g. date and time).
Other than that, use common sense. Don't store the equipment in a damp place, in a draught, or in direct sunlight.
I recently took out my EOS 5D that I put away about a year ago, turned on the power and it's ready to go.
Rechargeable lithium batteries last a lot longer, if stored at about 40-60% charge, rather than fully charged; you can then charge them before use, and they'll last a lot longer.
Regarding the equipment itself; A dry dust free environment will suffice, as long as it's not in an area that will see large or rapid changes in temperature or humidity (so avoid radiators, or direct sunlight)
I would store them all in cases/bag and remove the batteries and store them separate. If you are in a humid environment, I suggest using a dehumidifier or desiccant packs nearby to keep the humidity down and decrease the likelihood of mold/fungus. Also, make sure not to leave them in direct sunlight.