Some painters claim that an oil based primer may save you the hassle of removing the existing wallpaper but this is not the case. If a painter is giving you this information he is not looking out for your best interest and you should find a different painter. Although putting a coat of oil based primer may solve the problem temporarily it will eventually start to bubble and break down. Even though the process of taking down the wallpaper may seem tedious, it is well worth the labor in the end.
When removing wallpaper the first thing to do is to try to remove as much of the top layer as possible. Most wallpaper will have a vinyl top layer and a paper substrate layer. If done correctly the vinyl layer should peel off exposing the thin paper layer. DIF wallpaper remover should then be applied to the paper substrate and left to penetrate for 15-20 minutes. After allowing the DIF to penetrate it is time to scrape. There are multiple tools you can use for scraping the best being Zinsser Paper Scraper which allows you to scrape sporadically while not damaging the wall.
If the vinyl top layer does not come off so easily here are some other options:
Steam it -- This is the way that most people will remember from years ago. You can go to a hardware store and still rent one. With a steamer you just have to steam small areas at a time and then lift them as they come away from the wall.
Score it – A scoring tool, such as the Zinsser Paper Tiger, can be used to put small holes all over the vinyl top layer which will allow you to spray the vinyl directly and allow to DIF to penetrate to the wall.
Chemical wallpaper remover -- this one is a little messier because you will need to wet whole sections of the wall with it. This may sound harmful but it is not harsh on your hands. When you use this you can literally peel the wallpaper off with your fingernails (We wouldn't advise this though--a scraper is better on your hands and your nails).
Wallpaper removal sheets -- these are actually sheets of cloth that you stick on the wall and it is sprayed with hot water. Some people use hot water with a DIF mixture. The strips stay on the wall for about 20 minutes and then you can peel the wallpaper off easily.
As you are picking off the paper be sure not to just rip it off. Be gentle with it because you can damage the wall underneath the wallpaper. Once all of the wallpaper has been removed you will have to wash the walls completely and use an oil based primer before painting.