One thing I never read about tallit katan is how to wash them? Does wool need to be dry cleaned? Cotton can be handwashed. I guess I could handwash wool as well, but doesn't seem as good an idea. Any thoughts--- Especially for those of us who live where walking into a dry cleaner with a tallit katan is not a good idea.
The best way to wash a wool tallit katan is by hand washing it. Washing machines and dryers can severely mess up a wool tallit katan if you're not careful. I would suggest hand washing the tallit katan in a mild fragrance-free hypoallergenic detergent, in cold/warm (not hot) water, and then hang it out to dry.
If you have a trusted dry-cleaner, some have found success with taking their wool tallit katan to the dry-cleaners. (But you mentioned about dry-cleaners being a bad idea in your area.)
As for cotton tallit katans, you can actually wash those in the washing machine no problem. It would be a wise idea, however, to purchase a mesh bag to put the garment in, as well as a Fringe Guard tzitzit protector, to keep everything in tact while in the washer.
I should also mention that if you wear Radzyner techelet, you should never wash the tzitzit, as the dye will come out when in contact with water. If you wear techelet from the Ptil Tekhelet Organization, you have nothing to worry about, as the dye will not run out of the strings.
I also might add that I recently took an old wool Chabad tallit katan with silk corners to a dry cleaners, and the garment came out perfect, like it was new. I also might say that since there is no Jewish community out here where I live, it would be easy to say that they didn't even have particular experience with washing tallitot k'tanot. (But the garment did not have techelet strings.)
Wool needs to be washed warm, hot water will shrink it, usually.
Safest is to hand-wash them.
If you want to machine wash them, it's best to put the fringes in plastic bags (and poke a few holes) else they get tangled and may rip. Else put the entire garment in a sock bag.
Or use a tzitzit guard to keep the fringes safe.
If you can find a dry cleaner that will protect the integrity of the tzitzis, this would be the most ideal way to clean them.
Washing them by hand would be the second best. This helps in the following ways: the fabric of the tallis katan could become damaged or at least weakened by the spinning of the machine as well as the tzitziyos becoming tangled.
In addition to washing them by hand I would suggest using a soft detergent specifically designed for a tallis katan (assuming it is wool) such as Woolite.
After washing the tallis katan it is best if you can dry it quickly otherwise it will smell badly for some time until it dries. I would suggest hanging it in front of a fan until it is dry.