The first file is the style file.  Just \usepackage{thesis} and you
get that one. It should need very little modification, if any.

The other file is a latex outline - the one you should actually call
"latex" on to make the dissertation.  This one uses the thesis
package, a few other packages (like doublespace), and it also defines
a few things you have to fill in - places for your committee's names,
etc.  It automatically includes files called acknowledge.tex and
abstract.tex.  You can also include vitae.tex - check the end of the
file.

Each of the other files that are included should look just like latex
files except there are no usepackage or begin/end document commands.
I recommend doing your chapters this way, too.  They get pretty long.