Wet the sponge until it's slightly damp and apply to the wallpaper piece that has pulled away from the wall. The damp sponge softens existing adhesive on the wallpaper, making the paper more pliable.
Lift the piece of detached wallpaper slightly from the wall. Be careful not to create a fold in the lifted paper, or tear the edge. Any tears created can quickly spread across the width of the wallpaper.
Take the adhesive and apply it to the side of the wallpaper that faces the wall using the paintbrush. Coat the surface of the wallpaper completely, applying a light layer of the adhesive.
Press the wallpaper against the wall to glue it in place. Allow the adhesive 15 minutes drying time.
Go over the newly glued wallpaper with a wallpaper roller. Apply moderately firm pressure to roll out any air or wrinkles in the rehung wallpaper.
Remove any excess adhesive using the damp sponge.