Picture a 55 gallon reservoir, empty. Inside it sits a 1 gallon bucket with a pump and a pvc line that drains to whatever you want (sink, hose output, whatever). On the top of the rez, that also braces to the buckets PVC, is a pvc style square shower head that sprinkles water down. I just plug in a garden hose to it. Water in, dirty water out. You let the rez fill so all the loose particles drop to the bottom. Then turn on the pump and empty it all out, then let it stay on and rinse with new fresh water.
The bucket with the output water pump on it has a ton of holes so that water and junk goes in but not Hydroton. Pump also has a cage around it so nothing sinks through, but not permeable enough where small rocks will penetrate, they will just stay in the bucket instead since they cant get out of that either with positive pressure.
Uses 100 gallons of water to wash 55 gallons of Hydroton. Pretty good I think.
Its the same thing as me filling a bathtub, except a hell of a lot more automated lol........ You can DIY at home too it'd just take a medium amount of work cutting and drilling holes is all.