I'm not too experienced with DWC but my first attempt is looking good so far. I'll run you through my process in as much depth as I can and maybe that will help.
I had an aborted attempt at cloning in a dome with peat pellets. I think I had let them get too dry, but whatever the issue things weren't looking good. I decided screw it and ordered a DWC cloner kit from Daddy Bezos. Mine utilizes an air pump to oxygenate the water without heating it up.
I put the thing together as described and filled it up with tap water. I didn't pH or anything, and mine comes out at around 8.5 pH regularly. I chose the least dead looking clones I'd already clipped in peat moss and tossed them into net baskets to try and revive them. Additionally, I took another couple clippings from each plant I wanted to clone. I was not sure how effective it would be and wanted to get at least one good clone per pheno.
For a week or so I put on the included humidity dome and placed them into my veg tent with only one of the two lights on. Temps in there are around 72, a bit colder at night when I crank the AC. I check it once a day to see if the water level has fallen significantly, if it has I just refill with water from my plant reservoir. It's RO'd and has a bit of cal-mag in it, but the vast majority of my reservoir in the DWC is still just tap.
I didn't notice any significant root growth over the course of the week, and doing some reading I realized I could probably just take the dome off. I went ahead and did that a few days ago, and I'm not sure if it was their time anyway or removing the dome made a difference but today things are looking pretty good down there today!
That's about 12 days after putting them into the cloner.