I am sure your just takling about preserving the nest for display, so here is how i do it, may not be the very best way but works for me.
Go buy around two cans of that old sticky Aqua Net hairspray at the dollar store, or what ever and hang it up and start soaking it down and let dry and repeat till that thing is good and stiff. This stuff will not leave a shiney apperence and thats what you want. It was good enough for Grandmas' beehive hairdo!! haha.
Just don't smoke while doing it :0)