To begin, be sure that you have the following 
packages installed in your TeX distribution:
xifthen, setspace, datetime, xparse, graphicx,
etoolbox,
and (optionally) fncychap, along with the 
KOMA-script book class: scrbook.

Next, place the class file somewhere in your 
TeX path, preferably in your local directory tree.
In general this belongs to the variable TEXMFHOME.
The location of your local directory tree varies
by system, but is generally:
*Unix-like: ~/texmf/
*MacTeX: Users/<username>/Library/texmf/ 
	 The Library folder is hidden by default
	 on recent versions of OS X (>= Lion). 
	 This can be permenantly unhidden by 
	 issuring the command:
	 chflags nohidden ~/Library
	 at a Terminal prompt. On Mavericks, this
	 can be accomplished by accessing the 
	 Finder menu item
	 View >> Show View Options
	 and checking the box 
	 "Show Library Folder"
*MikTeX: Your local directory tree can be any 
	 folder you like, as long as you then 
	 register it as a user-managed texmf 
	 directory (see 
	 http://docs.miktex.org/manual/
	 localadditions.html#id573803)
Within this local directory tree, assuming your
TeX installation conforms to the TeX Directory
Structure (TDS), which most modern distributions
do, you should place the class file in
$TEXMFHOME/tex/latex/base

After installing the class file in the 
appropriate directory, it is important to check
that your installation of TeX can use the class
file. If you have kpsewhich installed, this is
as simple as entering:
kpsewhich uc-dissertation.cls
in a shell. Otherwise, you can copy and paste
the text below into an empty .tex file and try
to compile it.

--------------------------------------------------

\documentclass{uc-dissertation}
\begin{document}
Hello World!
\end{document}

--------------------------------------------------

If this doesn't compile properly, try to figure 
out why. It could be that TeX doesn't know where
to find the uc-dissertation.cls file, or it could
be because your distribution of TeX does not have
the required dependencies. 

Assuming this compiles properly, you are ready to
move on to the template. For instructions on how
to use the template, consult the dissertation.tex
file within the template/ directory. You probably
want to make a copy of this directory and start 
using the copy as the working directory for your
dissertation.

Happy TeXing! Oh, and good luck on that whole 
"dissertation" thing...  ;-)