Don't put chemical stripper on those walls as mentioned at your blog! It will tear them to pieces!!

I love spackle but that won't work for you, looks like the areas are too big. You'll need joint compound. You can get it pre-mixed. Were it me, I'd gently take a very thin flat metal putty knife, a 1" wide blade and maybe a 2" or 3" (depending on the size of the area), slide it under the peeling paint, hold the handle at about a 45 degree angle from the wall underneath and slide it under loose paint to lift it off, moving in a gentle forward motion. Use light pressure, don't saw back and forth. Just keep putting the putty knife under the paint and sliding it under the loose paint and nudging it forward, toward a stable section of paint. Be careful you don't gouge the wall worse! Do this till all chipping/peeling paint comes off and stable paint clings. If sublayers of paint are old, wear a good mask, you might be dealing with lead based paint. (You might want to google LBP for more info, just to be safe.)

Once all loose, chippy paint is off, use sandpaper to remove any loose chippy border edges of the old paint. Wrap it around a sanding block and use that so you get a good, flat result. Doing it by holding the paper in your hand won't get you a really level finish, as uneven pressure from your hand can cause uneven ridges on the wall. Smooth the edges so you get a smooth feathered (no definite ridge) transition from the old paint to the surface below. Probably start with 180 grit and repeat, moving up to 200. Wouldn't recommend going below 150 grit, it could tear up the wall worse.

Joint compound is tricky stuff. I don't like working with it. It takes me forever (I go slow and use multiple thin layers.) I am a neurotic perfectionist and I have tremendous envy of people who can slap the stuff on, smooth it out and barely have any sanding in just a few swift motions ;) You apply it with a drywall knife (blades from small to wide, as wide as 12" +, depending on surface area). Smooth it out as best you can with the knife. It's something you have to get a feel for working with. Don't glob it on, let each layer dry thoroughly (it will be chalky white, I let it set at minimum a overnight). Sand smooth with 180-220 grit and repeat in layers till you get a flush surface to work with. Small spots you can use spackle. That I can do quickly. Just apply a dab with a small (1" - 2") putty knife with a good beveled edge, keep it clean. In as swift a movement as possible once the dab is on there you scrape it flush. Start on good wall so knife is resting on flush surface, hold the blade steady and slide it right across the spackle and don't stop till you've reached and gone beyond good wall on the other side of the bad spot.

You'll need to prime, I like Zinnsser Bullseye 123, but you might want oil-based. It depends on what's causing all that chipping and peeling. That is the top priority, correcting that, because it could happen again. Is this a bathroom, with too much humidity? Moisture from the attic above? Any idea what caused that?

Hopefully one of the guys will see this, they can probably explain better than I.

Moon pretty much has it spot-on.

For further analysis...
Can you describe the room?
1) Age of home?
2) Plaster or Drywall??
3) Age of existing paintjob?
4) How good is existing insulation?
5) Any rooms above this?
6) An operable bath-fan?? Is ducting open & vented OUTSIDE??!!

>>> Sorry, but as Moon says...all that loose stuff has gotta come off. You're just wasting time & money if you don't.
If you go ahead and paint after only scraping, the new paint will just pull off the older stuff...it would only be a matter of time!

Faron