You know how, with glass bakeware, you can do almost anything to it? Bake it, freeze it, broil it. Scratch the crap out of it with knives and spatulas. Clean it with oven cleaner and steel wool. It's indestructable.
Unless you drop it.
Wool's a lot like that. It's pretty darn sturdy - there's a reason our ancestors have worn it for thousands of years - so long as you avoid a few specific things. Those things are temperature shocks, agitation, and alkaline/base chemicals.
Remember. Wool is hair. You have hair on your head. Don't do anything to your sweaters that you wouldn't do in the shower (like washing it in bleach). It's a good thing to keep in mind.
First, let's take a look at our fiber:
This is a scanning electron microscope photo of a wool fiber. In fact, it's a high-quality wool fiber; most are rougher than that. See the shingle-like arrangement of the surface? Those are often called scales, and are mostly, though not entirely, how wool felts together. In heat and moisture, the shingles open up a bit and hook on other shingles, and the whole shebang turns into one giant matted up clump. (Which can be a good thing, if you want felt. Felt's useful. But it can also be horrifying.) Agitation, scrubbing, wringing, that kind of thing all pushes the wool fibers together and helps them snag on each other. So no agitating. Lay wool in a basin of water and prod it as little as possible; let soap do all the cleaning action chemically. Several rinses will remove all the dirt after that, without you having to move the fibers much. (Incidentally, superwash wools are superwash because either the scales have been burned off, or glued down, so they can't hold on to each other.)
Shocks in heat make wool fibers contract and shrink. It's not heat that does it; it's the temperature difference. I regularly boil wool while dyeing it. It's not a problem, so long as you raise the heat slowly so the fibers can adjust. On the other hand, when I'm felting on purpose, I try to get the largest temperature difference possible between the wash and rinse cycles, occasionally going so far as to put ice in the rinse water. (You can also do a slower, less extreme version of felting by putting damp wool in the dryer and letting it tumble while on a hot cycle. That tumble/damp/heat combination is IT for creating felt and shrinkage.)
And last, alkaline solutions. In practical terms that means bleach and ammonia. Wool will completely dissolve in bleach (and I assume ammonia, which is almost as strong). So no bleach. However, nearly all soaps and detergents these days are ph neutral and perfectly safe. Anything considered particularly good for skin or hair is mild (has to be) and safe to use for your woolens. A note on detergents, though; they are chemically different than soaps and work by removing or breaking down OILS. Which means it can dry out your wool and leave it like your hair after a week at the beach with no conditioner. For occasional washes, especially if something's been worn a LOT and is really dirty, detergent is okay. But I don't suggest it as an every-time sort of thing.
So how do I wash wool? Fill up the washing machine (WITHOUT the knitting in it) with room temperature water and soap. (I usually use regular old laundry soap - Tide. I've also been known to use baby shampoo, regular shampoo, dish washing detergent, anti-bacterial hand soap, Woolite, and specialized 'wool wash'. I can't tell a difference, other than smell; the fibers are always the same after.) Once the water's done running, I put the knitting in, push it under the water, and hold it there until it quits bubbling. (Wool holds a lot of air in it; when submerged the air bubbles back out.) Then I leave the knitting alone for about fifteen minutes, though up to a half an hour if it's really dirty. Then I lift (carefully) the knitting out of the water and let the water run out of it; no squeezing or wringing. I put it aside, spin out the wash water, run the washing machine full of clean water (also room temp) for the rinse, and put the sweater back in (often with a bit of prodding to make sure the fresh water's getting all through the knit; poke carefully but still no grinding or wringing). Let it soak for another maybe five or ten minutes, then just turn on the spin cycle. The washer will spin the water out of the sweater, leaving it almost dry. Then spread it out in whatever form you want it to have when dry (think of it like styling your hair as it dries - same exact idea) and leave it alone. It should be dry in an hour or less.
I've never felted anything, using this process, though the husbeast once helpfully took a blanket out of the washer and put it in the dryer for me. It's now a potholder.
This may sound like a lot of trouble, but really it's like doing a load of laundry. You pop it in and forget about it for most of the time involved. And I LOVE wool - it's toasty warm but because it breathes, you can wear at least thin layers of it in warm weather. You can't beat it.