The easiest way to fill a hay net is to stretch the opening over the end of a bale rather than trying to wrestle individual flakes into the net one at a time. Once the net is full, pulling the drawstring closes the opening. Rather than wrestling with knots, the easiest way to keep the net shut is to pull the drawstring so that the knot sits against the rings of the hay net, holding them together. This also ensures that the knot will stay out of the way when you hang the net up.
Step two is to find somewhere to hang the net. Horse trailers often have welded loops set high in the trailer that are perfect for this purpose. In some cases, the bars on the trailer window have to suffice. In a stall, a hay net can be hung from a high bar (temporary show stalls usually have a bar that runs all the way around the top of the stall that is ideal for this) or through a screw-eye set high on a wooden wall. It's important to hang it from a high enough spot so that the bottom of the hay net will remain well out of reach of the horse's legs. Safety-wise, it's better to tie a hay net too high than too low. Aiming for wither-height or higher when hung should be safe. Once you have found a suitable spot, run the drawstring around the bar or through the loop and then pull the hay net up as high as it will go (it will slip down slightly as you tie it).
Keeping tension on the drawstring so that the hay net stays up, pull it down and hook it around a string near the bottom of the hay net. Pull the drawstring back up towards the top of the hay net, bringing the lower part of the net up with it.
Loop it back through the upper section of draw string...
...and tie a quick release knot to secure the hay net.
Flip the net around so that the quick release knot lies against the wall, away from the horse so that it is less likely to be accidentally untied by teeth.
This last photo illustrates why it's so important to double up the hay net by hooking the drawstring around a bottom string while hanging the net. As you add hay, the string diamonds that make up the net become wider, making the whole net shorter. As it empties, the diamonds end up with less and less width, making them longer until all of the string is hanging vertically when empty, making the net almost twice as long as when it's full. The doubled hay net will stay up high even when it's empty, while a non-doubled net hung at the same height will produce something like this red net, hanging dangerously close to the ground (both nets are the same size!):