Yeah, I admit it's a pretty nifty concept! Works perfectly, too.
I used a small net bag, mine came with those tiny mandarin oranges in it. Onions also come in them. But an old sock would work, too.
With the water bottle sitting upright on it's screw-in water base, slip the bag (or sock) over the bottle part. Tie a sturdy string as tightly as you can around the neck just above the screw-on threads. Take an "s" hook and slip it through the bag (or sock) at the top. The base is completely free to screw back onto the bottle after you fill it.
I screwed an eye screw into the stick I slipped through the slots I cut into the top of the brooder. I used carabiners to lower the bottle close to the floor of the brooder for the first week, and since the chicks grow so fast, I removed carabiners as the bottle needed to be raised to keep frisky feet from kicking shavings into it. The water tray needs to be about neck high to the chicks current size.
I forgot to add : there may be some excess material hanging below the string and into the water tray. Making certain the string is as tight as you can get it - test to see that it will hold a full bottle of water before you hang it in the brooder - you can trim the excess off with scissors. A flat cotton shoe lace works well for the tie since you can really get it tight.