This post is also cross-posted to spinningfiber, but I really genuinely think it's relevant across the groups. platys, feel free to have a word with me behind the woodshed if you disagree.
The first signs of wool moth infestations will be either the larval cases or the frass. I am only familiar with the casemaking wool moth; you may also have trouble with carpet beetles or webbing clothes moths. The casemaking wool moth larva spins a kind of silky cocoon around itself as it eats; this cocoon will basically be the same color as whatever it was eating, over white. I had a wool moth larva eat through leftovers of a ball of Opal self-patterning sock yarn, and you could kind of see the pattern show up in the case. The cases look like this:
If you find one of these and you're not hideously squeamish, squeeze it. If nothing happens, then the moth has already matured and gone off to find Moth Love in the rest of your stash. If bug guts shoot out the end -- congratulations. That particular moth won't be doing anything of note in the future.
Frass is wool moth larvae poop. It looks kind of like finely ground coffee; again, it will likely be a similar color to whatever the larva was eating, only darker. A quick spot check for moths is to agitate whatever your wool or your yarn is in, and then check the bottom of the container for frass. If there's frass, do a hand-search of everything in the container, and then go to the battling tips below -- even if you don't find anything.
Casemaking wool moth larvae tend to eat in a straight line, across the plane of something. When you're looking at balls or skeins of yarn, look for ends where there shouldn't be ends, or sections of yarn where one ply is missing or thinner. A badly infested skein may look fine, but simply fall into bits when you try to use it for anything. When looking at finished articles, the holes aren't huge and gaping at first, they just look like a place where your tension messed up, but under tension, will reveal the extent of the damage. In woven, fulled fabrics, they will often eat the raised fuzzy finish off the fabric, leaving it slick and shiny. In unspun fiber and roving, the damage is harder to see; if you really haven't messed with the surface of it, you may be able to see the groove where they've eaten through, but you probably won't. If your sample seems to have a much shorter staple length than you remember, wool moths might be the culprit.
When you find evidence of them, what can you do? The first step is to put everything into the freezer. I have been told that 48 hours in, 24 hours out, 72 hours in will kill all the moths regardless of life cycle. If you don't have six days, you can get the material soaking wet and put it in the microwave for, like, three minutes; the steam will surely kill anything on the fiber itself. But the moths don't just eat your yarn; they'll eat cobwebs, pet hair, YOUR hair if you leave it lying around, wool carpeting . . . so purifying your stash isn't enough. Mothballs will deter the larvae but won't kill them; lavender and cedar oil will apparently do the same thing, but the scent must be strong. Fumigating your house with toxic insecticides will do the trick, but you might be reluctant to take that step. (I know I am.) Once you are sure that yarn or fiber is free of moths, you can store it in an airtight heavy plastic bin; moths can chew through thinner plastics, but anything much thicker than a freezer bag will deter them. If you live somewhere where you have access to an extremely hot attic (110 F or above), you can put everything up there for the summer; similarly, if you live somewhere where it freezes hard and you have an unheated garage that will get below freezing for a week straight, you can keep it there.
I live in balmy Seattle, and I do a complete wool inventory every three to six months. I do the freezer or the microwave treatment with anything I find frass or larva cases in, and if something is heavily infested, I pitch it -- it's just not worth it. I also investigate carpeting in closets, my sock drawer, and anywhere else I have things made of wool. Under the couch where the cat fur bunnies live is often Moth Heaven, and ever since I noticed that the cob spiders will trap and eat the moths, I've become a lot more sanguine about letting them hang out in my corners. The adult moths are tiny, smaller than a pinky fingernail, and very hard to notice, but those larvae. . . . once you know what they look like, you can spot them across a crowded room, as well as the frass. Look over new purchases carefully before you chuck them in with the rest of your stash; maybe consider quarantining for a while, just to make sure. I am very slowly winning the war against the moths, but it's a long and bitter battle, and my victory might well be Pyrrhic.