The class has a number of required fields, without these it throws various errors including claiming that the preliminary environment is not defined. You can almost find all the requierd fields by looking directly in the class file gatech-thesis.cls, but that misses that some adviser is needed too. The following is a minimal document that will compile:
\documentclass{gatech-thesis}
\begin{document}
\title{Profound title}
\author{A. Student}
\department{Department of Mathematics}
\degree{Doctor of Philosophy}
\gradyear{2013}
\approveddate{\ }
\principaladvisor{A. Fields Medallist}
\submitdate{Tomorrow}
\begin{preliminary}
\begin{abstract}
Test.
\end{abstract}
\end{preliminary}
\end{document}
Note that e.g. \approvedate must actually print something (here a space), an empty argument is not enough. I guess the class does it this way to enforce the particular rules of the Georgia Institute of Technology.
gatech-thesisdo you have? The version on CTAN is v1.7 in the.cls(although the README suggests a combination of v1.5 and v1.8) and does include thepreliminaryenvironment. – Werner Mar 4 at 18:20\titleetc. but also things like\approveddate. – Andrew Swann Mar 4 at 18:23preliminaryenvironment. It'll help speed up getting answers. – Werner Mar 4 at 18:23