From what I know, there are two ways to get items:
Network: Somehow get to know cast members, technicians, producers, creatives. The more the better, put some leverage in. Use these connections to get small things, ask if they can ask to get that fake dagger that gets thrown out every night or the crumpled paper prop that is recycled every other week. At the end of the run you can try to get bigger things for example a railing or some curtians.
Look: Dumpster dive at the end of run, I know a member here did this for In the Heights and found the milk carton that Unsnavi smells in the first song. If you prefer to keep clean, look at the flea market. I think someone here got the Phantom's chair there as it was being replaced.
These are the ways that I know of to get items but it is a shame that so much must be wasted. Here are articles on the subject of the recycling initiative:
http://mobile.nytimes.com/2009/02/15/theater/15davi.html?referer=&_r=0
http://mobile.nytimes.com/2008/11/26/theater/26gree.html
I appoligise for any spelling mistakes. I may be on my mobile. Clumsy fingers and small little touchscreen keys don't mixx. I try to spellcheck, but I may miss something.