One of the things I love about traditional archery is re-using the same arrows and broadhead to kill multiple animals. Back in my compound days, it was once and done with the broadhead/blades, and usually the plastic fletching got a bend I it, so I ended up having to refletch.
I haven't seen a post on this, so I thought I would describe what I do, then anyone with easier or more nifty ideas on how to do it could chime in.
If at all possible, I was the blood off of the fletching immediately, and certainly try to do it before the blood dries if I can. This can mean using a water bottle in the field, and often it means dunking the fletching in a stream and swishing it around and rubbing the fletching with my fingers. The shaft can really be taken care of at any time, but I will do it in the field if I can. I prefer not to put bloody arrows in my quiver if I can avoid it.
When I get home, I will do a more thorough job in the sink, and I will use scent free soap if I have to (usually only if the blood has dried some). If you don't get all of the blood out, the fletching will not separate well when drying, in which case, I start the washing process over. I use my fingers or an old toothbrush to get any dry blood from the fletching wraps.
I take the broadhead off and wash both it, and the shaft, then put the broadhead back on the shaft, although I suppose you could put a field tip on. I will then spin the excess water off of the fletching by spinning the shaft as if it was a fire starter, between my two hands. I either do this outside, or I put the arrow and my hands I the shower, using the curtain to protect me and the bathroom, and keep my wife from beating my.
Then I put the arrow in the bathroom sink, tip down, and break out my wife's hair dryer. I use this to blow air on the fletching, while spinning the upright shaft with my other hand. Eventually it will get dry enough so that the air from the hair dryer will spin the shaft, very fast actually when near dry. Along the way, I am trying to keep the fletching from laying down to flat, or be sticking out so much that there is space between the feathers. I would probably rather have it stay a little flat and the toward the end gentle pull against the grain to raise the fletching when it get closer to dry, but you have to make sure there is no blood holding them together.
After that, I sharpen the broadhead and put it back in my quiver.
Now, I would love to hear what others are doing.