I have to tell you plowing through the U.S. government copyright web site is not for the faint of heart. The information there. They do give you the basic facts but they do skimp on the graphics that would make the concepts more clear.
Fortunately Michael Brewer and the American Library Association's Office of Information Technology has come up with a visual way to understand what works are in the public domain and what works maybe under copyright protection. Check out the Library Copyright Digital Slider.
June 2012 Update: The Copyright Slider has been replaced by other tools at the American Library Associations Copyright Advisory Network. web site. This post remains but there are new tools you can use.
The Good News:
Public Domain means that the content, also referred to as "the work" (text, book, movie, music, etc.) is no longer protected by U.S. government copyright and can be used by any person for any reason. So a movie made in 1916 could be incorporated into your video without asking for permission.
It get better. Works created by the U.S. government for the benefit of the citizens are also in the public domain. Those NASA photos and movies, you can use them. That old timey sex education movie made by the Department of Defense for soldiers in World War 2?
You can use it and there is no date restriction. So if there is a rocket launch that would fit in your video you can use it. However attribution is a wonderful thing so cite your sources in your closing credits.
Where It Gets Tricky:
Anything after 1923 you will have to investigate. According to the Digital Slider, if the work was not renewed for copyright protection between 1923 and 1977 you are good to go. But you have to find out about the status of a work before you use it.
The U.S. Copyright Office is happy to help but it will cost you money.
And it gets trickier when a work does enter into public domain status and someone copyrights their version. Their implementation is copyrighted but the source material is still in the public domain. You can use the content and create your own interpretation of the work.
For example. The story of Cinderella has been told by many cultures and was created long before Walt Disney picked up a pencil to draw the animation.
You can tell a "Cinderella" story but you cannot use the movie, music or character likenesses of the Disney animated version. You have to create your own interpretation. To be on the safe side, leave Cindy out of it.
Yes, I know - Fair Use. A discussion for another time.
I'm not a lawyer. If it is really important to get it right you might have to consult one. But this is a good way to figure out if you can or cannot pop that musty dusty of a tune into your video.