We travel quite a bit, and for long trips, 2 or 3+ months. We send a fair amount of laundry to have it done when we are stationary for a few days, but there is quite a bit that I don't want ruined so I hand wash regardless of the time frame.
If only small amount, I hand wash in the sink, larger amount I hand wash in the shower, very easy. I also have a collapsing bucket that takes up no room and works really well when you have a too tiny sink.
I don't have a drying rack, but I did make a really handy clothes line that I can attach most anywhere and adjust the size dependant upon space and needs. I made it with ball bungie cords, I love my clothesline. It is so much better than what you can buy at REI, etc.