The basics of caring for any hand-dyed item, regardless of the fiber content or type of dye, are going to be the same: Hand wash in cool water with a mild detergent, gently remove excess water, and air dry.
At home, I fill a sink with cool water and Eucalan, submerge the items and gently work the water through them, and then let them sit for at least fifteen minutes. Eucalan doesn't need to be rinsed, so I squeeze the water out (don't wring, it can damage wet fibers!), roll them up in a towel and squeeze to get as much more as possible, and let them air dry on a lingerie rack. Any wrinkles can be pressed out with an iron on the appropriate setting.
With any dye process, there will be excess dye particles that don't bond to the fibers and cause rubbing off (also called "crocking"), or bleeding. I do several things to try and get rid of as many of those as possible before something leaves my house, from using fixatives to multiple wash/rinse cycles, to trying to not get as many extras on in the first place, but no process or person is perfect. I recommend washing a piece with similar colors or by itself the first few times, which should be enough to get the last clingons off. If it continues bleeding or crocking after a few washes, please contact me and I'll work with you to stop it or replace the item.