The simple trick: Wash in cold water and line dry!
I drape my washed sweaters over a quilt rack that we have in front of the fireplace, and this works nicely. My sweaters are generally dry within 24 hours.
I have not had a single issue with my sweaters or pants shrinking or the fibers changing texture by doing this. The only inconvenience is that my sweaters sometimes get those little fuzz balls on them after a few washes, but we have this nifty little device that was less than $5 to get rid of them.
It has been my observation that many of the sweaters I’ve purchased from the thrift store are dry clean only. I wonder if people were tired of paying the dry cleaning bill every month to get their clothes clean.