Gather from multiple sources. Obviously, get a playbill from any show you personally attend, but also consider asking family and friends that visit Broadway to get you a copy. Ebay can also be used to buy playbills, or in some cases, playbill collections from others.
Preserve and display your collection. Options include sprays that will keep the paper from yellowing, polyethylene bags, airtight display cases and framing. A combination of one or more methods might work the best for you, such as anti-yellowing treatments and framing.
Provide quality storage for your collection. Chances are, you don't have an entire room of your house dedicated to display cases for your playbill collection, so you might want to consider rotating parts of your collection in and out of frames or display cases. The others should be kept in airtight containers and stored in a cool, dry place.