Removing wallpaper can be a real pain. You can paint over it, but this has some real problems. Like, still seeing the seams through the paint and it is possible that the primer and paint will cause bubbling of the paper from the wall.
Here's a few suggestions for stripping wallpaper:
1) Remove the top layer of paper first, leaving the paper backing on the wall. Most of the time this is easy. Simply use a finger nail or putty knife to get under the paper and pull it off.
2) Usually plain warm water is all that is need to loosen the wallpaper backing and glue. Use a garden sprayer or similar device to wet the paper and keep it wet. Wait for 30-60 minutes before trying to pull off the wallpaper.
3) You can use wallpaper stripper mixed with the water. Often this isn't needed but can help if the glue is particularly difficult to remove.
4) Do not use devices that puncture holes on the paper. These can help but they also put small holes in the wall surface. These holes will need patching before painting and there will be thousands of them. If you decide to use one of these devices, be careful and don't use a lot of pressure.
5) Use a 6 inch wide drywall knife for the removal. Be careful not to cause any damage to the wall.