I repeat...do not paint over it. you will regret your decision in no time at all. You have to remove the paper and the backing and then possibly scrub the walls to remove the residue. I highly recommend using a product called DIF and a good wallpaper scraper. It will take you a while, but you won't have to redo it.
By the way, I just removed that wallpaper from every room in my new home and the paper was there much longer that 30 years. It was a pain, but it will never look good if you just paint over it. Wallpaper was a bad trend, but laziness in removal of it will produce even a far worse sight.