There is no built-in way to take screenshots in Psychonauts. Here is some free screen capture software I'm aware of (included in
this superb list that you might want to bookmark):
http://taksi.sourceforge.net/
It's open source, which is usually a good phrase to include when searching for free software as it almost always means there's no ads, no trial limitations, etc.
It does video too, but not with audio.