How would I approach modifying the administrative backend tool for Movable Type? Is there a set of files that I need to look at? Is there online documentation available? I am interested in adding additional fields to some of the sections.
I am using Movable Type version 4.21-en.

http://www.movabletype.org/documentation/developer
If you want to modify the functionality, the only sane way to do it is through plugins.