Whoever it was in the decorating industry who decided it was OK to paint over wallpaper should be hung over a shark tank by their thumbs! It is the most frustrating mess to remove. But at least you are lucky to have plaster walls... this is a nightmare over wallboard. The plaster will endure process.
Rip off as much of the "surface" wallpaper as you can. It may leave behind a backing on the wall, but that's ok, as it's much easier to remove than the painted surface paper.
The first ESSENTIAL tool you'll need is something called a Paper Tiger. You can find them at anyplace that sells wallpaper, and even some discount stores like Wal Mart. They are basically several small, toothed wheels in a plastic handle. You run the Paper Tiger over the surface of the painted paper VERY GENTLY to put small holes in the paper (do not press too hard or you will find your plaster full of nasty little indentations when the wallpaper comes off). The holes will allow the wallpaper remover to get through to the back side of the paper and release the glue from the wall.
Depending on the age of your wallpaper, the glue can be varied. Prior to WWII, wallpaper glue was made from the most remarkable things (boiled potatoes, watered down horse glue, shellac, etc.), so it's hard to tell what you'll find. I have even discovered several types of adhesives used in one room. If you have newer wallpaper (1970s and beyond) you may be in luck. Most of the newer glues are water soluble.
The first remover to try is plain old HOT WATER. Get yourself one of those cheap pump-type garden sprayers, fill it with fairly not water (not scalding) and set to spraying the paper, working in reasonable sections (perhaps floor to ceiling and 4-5 feet wide). You'll need to saturated it pretty well, so put a lot of old sheets or towels at the base of the wall to catch the runoff. Keep spraying the paper as it absorbs the water for about 15 or 20 minutes, and then use a metal WIDE-BLADE putty knife to gently try and lift the paper away from the plaster. You should NOT have to scrape too hard or you'll mar the plaster surface. If it's not coming off, more water is generally the answer. However, you do want to be a little cautious about getting the plaster underneath so wet that it gets mushy. (Plan to let your plaster walls thoroughly dry for several days before applying another wall technique.)
If the hot water method doesn't work, there are some wallpaper remover potions at the hardware stores you can try. Basically, they work with the same application method (score the surface with the Paper Tiger and then saturate with the product). I have not found that any of them significantly reduced the amount of sheer elbow grease involved in this project, and I have stripped 9 rooms of wallpaper to date so feel I am up on the subject. After the 3rd room and several of these projects, I just saved my money.
You can also invest in a wallpaper steamer. I have one made by Wagner and it does work pretty well. You will find that the steamer has a tendency to FIRST lift the paint from the paper (especially if it's latex) and you'll have to scrape that away before you can then steam off the paper. Also, with the steamer you are generally standing on a ladder for hours at a time and holding the steamer plate to the wall, moving from small section to small section every 2 or 3 minutes, until you think your arms are going to fall out of their sockets! And then you still have to use those now-sore shoulders to scrape off the paper and backing. Even if you use a steamer, I would still highly recommend using the Paper Tiger first.
Anyway you look at it, removing wallpaper that has been painted over is a time consuming, messy, backbreaking job. And, if you're REALLY lucky, there's only one layer! Have fun.