Chad's advice is excellent.
Wallpaper removal is hard messy work....AND you DEFINATELY want to remove it before painting. Painted wall paper doen't look good, plus it tends to bubble underneath, peel at the seams, etc.
I have had painted wallpaper removed from over 60 historic apartments.
I tried scraping it myself a few times. Sometimes it is easy, but most of the times it was just about impossible. Usually, I ended up hiring my friend, "Glenn the Painter" to do it for me. He is a lousy painter, but incredible at stripping wallpaper!
The only things I have to add is
1. He uses vinager mixed about 50% with the hot water when spraying. The vinager helps dissolve the old paste.
He sprays several times with a large pump sprayer and saturates the paper for an hour or so before scraping.
2. For a scraper he uses a 4" scraping knife with a razor type blade insert instead of a putty knife. He changes blades very frequently too. It does gouge the wall sometimes, but that is very easy to correct with joint compound.