OK, I've never grown quinoia, don't even know how to spell it, but here is what I would try:
Pick the stalks when the seed heads are still intact, but pretty dry/ripe. To test this, I guess you could try crumbling a seed head. You cold try chewing a few of the developing grains.
Get the seeds off the stalks by? laying out a tarp or sheet or something on a hard area or on the floor and walk on it. This is how I saw people getting the seeds off the stalks for a tiny grain called "fonio" in Senegal. They built an outdoor earthen floor and walked on the grain stalks.
You could also put another tarp or sheet over the top of the grain and use a flail, a handle like the handle part of a bat, with a flat piece of wood attached........ you swing the handle and beat the grain with the flat part..... I bet there is a You Tube of the process, in fact why am I writing this? I bet there is a you Tube showing the whole process, but anyway,
Then you get to winnow it. There will likely be some husks around the seeds/grain. When you walked on or flailed, you loosened it. So the huuks are lighter than the seeds, and you can set up a fan and get the airflow just strong enough to blow the chaff away but let the grain fall, and you get to pour bowls of grain down and let the chaff fly away.
Then usually before cooking, you need to wash it. I bet there will still be some chaff/husks left even after you wash it and some floats away.
It just might be a very satisfying process. I hope you have fun. Try the You Tube route. Then you'll know a person isn't just making it up, like I am.
The method in post #2 above is pretty much how I've done it.
About the easiest way I've found of separating most grains from the stems/stalks/heads/chaff/etc is to put them into a plastic kiddie pool and stomp on them. Then remove as much of the course debris by hand or with some kind of sieve/screen, and use wind power to remove the chaff. Pretty easy, really.
Patrick Mann wrote: What about washing? I understand there's a bitter coating that is washed off from the quinoa you buy at the store.
Yes, many kinds of quinoa have saponins similar to those in other plants such as Soapwort, and they can be very bitter. You can rinse it under running water for about 10 minutes to leach them out. I wouldn't try doing that until I was ready to cook it, because it would mean the extra step of drying it out again.
When I last grew quinoa, in 2009, I grew a strain from Seeds of Change that was specifically bred to be very low in saponins, so it doesn't need the leaching step prior to cooking. However, in browsing their online catalog, the variety they have now isn't it. I seem to recall it was called something like "Dave's Select Brown" -- or something with Dave in the name of the variety.