I sort of agree with Henry, but you can get good results painting over wallpaper. Problem is, it's just as easy to remove the paper as to prep the wallpaper properly for painting. Here is what is involved:
1. Remove any loose wallpaper sections.
2. Skim-coat areas where you removed loose paper with joint compound.
3. Skim-coat all seams with joint compound.
4. Lightly sand skimmed areas
5. Prime with a pigmented shellac (Zinsser's B.I.N. is great).
6. After priming, you may find a few areas have bubbled up. Peel off the bubbles, skim-coat those areas, and re-prime.
7. Paint with a good quality interior latex like Pratt & Lambert's Accolade or Pittsburgh's Manor Hall.
Now, removing the paper could take as little as a few hours. I found this great product by 3M at Home Depot. It's a green gel that comes in a gallon jug. I just glopped it on my bathroom wallpaper (no scoring unless the paper is vinyl-faced) and the paper peeled off in one big piece after letting the gel sit for 15 min. Wipe the walls down with warm water after the paper peels off (to remove residual glue) and you're done.
So, you CAN get good results painting wallpaper but it can be just as much work as removing the paper. And when you remove the paper you will definitely not have any problems later.