Remove as much of the wallpaper paste from the walls as possible by scrubbing them with a sponge dipped in wallpaper remover. Wear rubber gloves while working, and rinse the walls with clean water and allow them to air dry.
Use a sponge sander to work on tough areas. Once you have removed as much paste as possible, use a drywall sander to smooth any clumps down. You'll want to remove or smooth away as much of the paste as you can.
Apply a coat of acrylic primer over the walls and allow it to dry. Follow the manufacturer's instructions for drying time and to determine whether you need a second coat.
Check that the primer has thoroughly dried and begin painting the room. Follow the instructions recommended by the paint manufacturer for drying time between coats and to determine how many coats of paint to apply.