A fresh coat of paint not only freshens up your bathroom's decor, it protects the walls against moisture and can even help prevent mildew. When there's wallpaper already on the walls, however, it's necessary to remove it as well as any adhesive clinging to the walls before painting to get a smooth, professional look.
While some wallpaper will easily peel away from the wall with just a little tug at the corner, most will need to be soaked with remover and scraped away. Test the wallpaper by pulling the edges. If it doesn't come away easily, use a scoring tool designed to open small holes in the paper without damaging the wall behind it. Turn off the electricity to the room, and spray the walls thoroughly with a wallpaper remover, following the manufacturer's instructions, and then gently scrape it away in sections using a putty knife. Be careful not to gouge the wall while scraping. Sanding the sharp corners of the putty knife can dull them and prevent wall damage.
Painting over adhesive is a bad idea for several reasons. The uneven texture will show through the paint, it may cling to the roller and create globs in the paint, and it will become extremely difficult to remove once the paint has dried. Once all the wallpaper is off, spray the adhesive again with wallpaper remover and gently scrape the adhesive away from the wall. Use a damp rag to wipe the scraper clean as needed and work in sections, removing all of the adhesives from the wall.
Once the wall has dried completely from the adhesive remover, patch any holes and sand any rough spots. Pay special attention to areas where the wallpaper seams once were since even after the adhesive is removed, there tend to be high spots that need to be sanded. Clean the wall with a damp rag to remove any dust created by sanding. Tape off any adjoining walls, cabinetry, door or window frames or any other areas that won't be painted with painter's tape.
Choose a paint suitable for use in the bathroom, such as a satin or high gloss. Flat or matte paint or even low-luster paint like eggshell does not stand up well to moisture and can be difficult to clean. Some paints designed especially for the bathroom contain anti-mildew components. Select a primer that works with your paint, such as a water-based primer for water-based paint or an oil-based primer for oil-based paint, and apply a thin coat of primer to the walls. Let it dry, and then apply two coats of paint, letting the first one dry before applying the second.