When I first started working
with chicken wire my main method of attachment was using a staple gun,
which works fine, but sometimes those staples will work loose over
a few seasons if there's any pressure on it.
Now I use small drywall
screws like in the picture above. It's pretty easy to wrap a few turns
of wire around the screw before you completely tighten it down, and if
you ever need to change anything it will be a lot easier to take back
out compared to staples.