I've washed a bunch of domke's. Get a clean five gallon bucket or something, fill it with cold water and a bit of dishsoap. You're just using the soap to clean the water, not to clean the domke, so to speak. You could even leave the soap out, if the domke's new, probably a good idea. Put the domke in and squish it around, add some more water, let it sit, go back and squish it some more. Fill up the bucket with just cold water and squish the domke some more, dump out the water and repeat with clean water two more times. That's to wash the soap out, so if you never used soap, you can skip that. If you have back problems this might not be the best thing, I do it in the tub, it's a lot of bending and dumping a five gallon bucket.
Hang it in the shower to dry a bit. Squeeze it a bit, don't wring it or anything. Take it out of the shower to dry when it's pretty much done dripping.
It'll take about three days to dry. I don't put it in the dryer, myself.