For general infomation, check out www.pdinfo.comAnother source is Stephen Fishman's book The Public Domain.
Another place to check is
here. (Link no longer works. Here is the Internet Archive version. Update 2025-03-28)
And, as McGrath said, you can post a query here at the Mudcat on the origins of a song. If it's an old or traditional song, the chances are reasonably good that someone on this list can tell you where and when was its earliest known publication.
T.