If I'm doing a load of laundry I'll put them in there for the wash/rinse cycle (delicate) then hang them up to air-dry.
I'll also occasionally wash by hand in a bucket of soapy water - put 'em in, knead them a bit, let them sit, knead again, rinse, wring dry, then hang to air-dry. I've also done this in hotel rooms; the polyester materials seem to dry quickly, so if you wash them in the sink when first checking in they should be dry by morning. I also wash gloves this way.
I just wear t-shirts when out riding, I don't own any cycling-specific jerseys.