What have you found to be the best way to wash tzitzis (i.e. easiest, least likely to invalidate, and most clean)?
A few suggestions:
Tie your own tzitzis using the thick tallis strings.
When possible, try to hand wash them. Try not to get the braid and strings wet at all.
If washing them in washing machine, wrap the entire braid and strings in aluminum foil.
Hand wash wool tzitis in Woolite
When you first get/make tzitzis, dip ends of strings (each separately) in no-fray glue (available at any sewing supply store)
Since I'm using a cotton beged, I use the washing machine, and I put the tzitzis in a delicates bag. Then I hang the tzitzis to dry. Using this method, the tzitzis tend to outlive the beged.
I haven't figured out what do do with a wool beged. I have three that have been essentially ruined by the washing machine -- the fabric has shrunk and become very itchy.
I haven't had a lot of success, but the best results are when I tie the ends of the tzitzis and wash them tied in a pillow case. This probably would work better with a nicer washing machine with a good gentle cycle. I usually hand wash, but will this will keep the garment "clean" it doesn't do much for making it look "clean".
Cotton beged here too.
I put each corner's strings in a plastic baggie and rubber-band it shut. When it works well, the strings just get a little wet -- enough to clean them, not enough to destroy them. But it's labor-intensive. To remove the baggies, I usually just cut the rubber band.
Then hang dry. The strings will be all tangled up -- DO NOT TRY TO UNTANGLE THEM WHEN WET!! (Way too fragile.) First let everything dry -- then untangle.
Great trick for keeping zizit from tangling.
My wife takes my cotton begged zizit and washes with other clothes, buy she has a great trick for making sure the actual zizit strings don't get tangled.
She takes the four zizit and puts them inside a sock, then makes a knot of the sock, with the zizit inside and tosses it in the washing machine with everything thing else. We hang dry our clothes so I don't know if this will work for the dryer.
Regarding my talit gadol, I just got it back from the dry cleaning. It was cleaned but it came back all frayed and the zizit are unraveling and it is all wrinkled, I have a feeling they washed it in a machine and didn't dry clean it. I'm very upset and I sent it back for them to iron out at the very least. Now it looks like an old wrinkled rag. Thoe beautiful knots going around the edges of the talit gadol are unraveled and not tight like they used to be which reminds me of an old talit. It's only 5 years old....