The following video, filmed at Princeton Theological Seminary (and areas round about), is a fun little 5-minute exploration of what it is like to read Herr Karl. It includes moments with archivists, Dr. Bruce McCormack, PhD students, and even an MDiv student who very honestly notes how it is difficult to enter Barth's corpus. There are some little pointers and book suggestions throughout the interviews that are pearls for beginning to read Barth.
And as an additional treat, here's another 5-minute video on Barth's theology:
