'Green' alternative to TSP for cleaning walls for paint preparation
It's not easy but it provides a piece of mind. I've just been using 3M sponges with scrub-pads and Meyers Household Cleaner.

I've peeled the wallpaper in three rooms and followed up with a good scrub. Let it Dry. Then spackle and sand spots (120 or finer) that need it. Let that Dry. Then sand patches and lightly sand whole wall. Wipe down with a damp sponge rinsing out dust as you go. Let Dry. Paint with two coats.