Q: Is BE a program one can undertake on their own, or is it something best done with a teacher?
A: The Balanced Embouchure is a self help book written for trumpet. Most trumpet & horn players learn it on their own with a little email support as required. A few people have difficulty learning from books, so for them there's the opportunity for skype if there are no instructors in their area. I've heard some say that having an instructor helps them catch on more quickly. Jeff has a list of BE friendly instructors on his website. http://www.trumpetteacher.net/teachers.html
I learned BE directly from the book with support from The Balanced Embouchure forum in The Trumpet Herald. The BE forum is monitored by Jeff Smiley. http://www.trumpetherald.com/
Q: What supporting materials are there for somebody who wants to look into it? Books? Videos? A Web site?
A: The BE book comes with a CD of the exercises played by Jeff Smiley's young students (they're amazing, too!). The BE book is well written & provides detailed illustrations. With very few exceptions for placement of harmonics in the range, BE works exactly for horn as it does for trumpet. I distribute the BE exercises adapted for horn as well as other supplemental materials, for horn players to anyone who owns the BE book regardless of when or from whom the book was purchased. My adapted exercises are available as a PDF email attachment or as a bound booklet for $3.00 (to cover printing costs).
Since Jeff Smiley discourages BE students to copy the "look" of another's embouchure, there are no "official" videos provided for BE study. However there are a few recordings of enthusiastic trumpet players who have published YouTube videos of themselves performing BE exercises. Steve Park and I have put together a little video with a few of the basics of BE on horn, mostly to encourage horn players by showing that BE exercises can be done on horn. The link to this private video is available with the purchase of the BE book.
There are several links on the right to helpful sites provided by Jeff Smiley and other trumpeters discussing The Balanced Embouchure.
Hope this helps, Kerry.