How on earth do you get wallpaper off that has been put on unpainted drywall?

With great difficulty and limited success, sorry to say. It might be easier to laminate 3/8 drywall over the existing wall, adhered with construction adhesive.

You'll remember to prime it before putting up wallpaper, won't you?

It was the people we bought the house from, not me. The good thing is it's only one room! The bad thing is I've already gouged the drywall getting frustrated! Is there ANYTHING to make it any easier?

Low yield nuclear weapons?

A big picture of magaritas <sigh>
No wait, I would then throw the limes at the wall in frustration.

A streamer (and paper tiger) didn't work?

Most times wallpaper on raw drywall stays super tight. Why not leave it on and go over it? If you are going to paint, use a stain blocking primer like Kilz or Zinsser 123 to hide the pattern. If the seams show, trim them with a utility knife and skim coat them with drywall mud.

Patience and lotsa water. I have removed wallpaper from walls that weren't painted and it takes time but can be done. Buy a garden sprayer. Put down lotsa plastic sheeting on the floor unless you plan to rip out the carpet. Fill the sprayer with some detergent and warm water. Keep spraying the wallpaper. Keep going and going keeping it wet until it bubbles. You may need to score the wallpaper. Do this one section at a time so that while it is wet when it bubbles you can take a putty knife and scrap the wallpaper off. I won't lie - you are going to learn the fine art of skimcoating. It can't be helped. I would not paint over it though. At some point in its life the seams will start to show through the paint. When that happens you then must get paint and wallpaper off! Oh and when you do get the wallpaper off you may need to sand the glue off the wall. This can be done with a palm sander - just don't go crazy.

Good luck and stick with it. The margaritas might help considerably :-)

If the wallpaper is tight to the wall, you can seal it with a product called guardz made by Zinsser. Two coats are best. Once sealed, you can patch any rough spots or skim coat the entire surface and nobody but you will ever know. Once skimmed, prime and paint. Good luck!