First, wipe down with a clean microfiber cloth or a dusting swiffer. Then mix mild soap detergent (I prefer blue Dawn) in warm water. Then use a clean microfiber cloth or other soft medium to wash them down. Go top to bottom and be mindful of water dripping on the floor. I usually put down a cheap plastic table cloth from the dollar store.
You can wash painted walls with a soft cloth, warm water and a mild detergent.
White vinegar and water solution. First I dust the walls, then wash. I live in a hot, dry and dusty location, so I wash often. I purchased an industrial sized swiffer type mop at a restaurant supply with washable microfiber covers which makes it much easier to do.
Since interior walls don't get as dirty as they did in coal burning furnace days, the advice to wash from the bottom up is not so important as it once was. I seem to wash "sectionally" That is, if I am hanging a pic or paying attention to one section of wall, I wash that off with any kind of cloth I use for wet chores (usually a piece of old toweling) rather than attempting an overall wash down!
Beverly: I learned this by accident... I was getting some smudges off a (latex) wall with a Mr Clean Magic Eraser... it worked great! ...too great... the rest of the wall looked dingy! So... I cleaned the entire wall with a couple of erasers! Win!
Magic Erasers are actually made of melamine foam, which has been used for decades as an insulation and soundproofing material. About 10 years ago, someone discovered that melamine foam was also an effective abrasive cleaner, which acts like a refined sandpaper. That is why it cleans so well. I have used them in the wrong spots and they leave marks.
If you want to clean your walls and have a swifter, just use that to dust them down. If you are cleaning the kitchen use KrudKutter and a microfiber cloth.
Hi Beverly: Which ever way you choose to wash your walls, one tip is to wash from the bottom up. The dirty water will leave streaks on the dirty bottom part if you start at the top, and you will never get them out! If you start at the bottom and the dirty water runs down, it won't hurt anything. I use warm water and Spic N Span to do my walls:) Good luck