Rub down to remove all bit of glue and paper from the walls. Wipe over Vac. up dust and away you go......
Clean it well to remove the wallpaper glue. I like to use a bucket of water with vinegar in it and a sponge. Wash it until the slimy feeling is gone. Then wash it once more with plain water. Hot water dries the fastest.
If you have to make repairs, do that when the wall is dry. I like the spackle that goes on pink and turns white when dry. Prime those spots or the paint will absorb funny and be noticeable. Then you can paint.
In England we use sugar soap and a sponge to clean then when dry lightly sand any rough areas. If holes need filling use a filler for small cracks. Rub over when dry. Wipe off any dust.