You can view these files from the directory listing in your Web browser. You can grab the entire contents from this InfoZip file that you should be able to unzip on any modern platform.
The file uuthesis-2016-guide.pdf documents the new practices and typographical features. It has associated source, style, and spelling dictionary files as well. A template for a new thesis can be trivially scraped out of those files if needed, but it is better to start with one of the three sample theses, each in its own subdirectory. Each has its own Makefile to provide a from-scratch-to-PDF production process with a single invocation of the make command. Each also has a README file that sketches the steps needed to compile the thesis into a final PDF file.
The file Makefile is a sample Unix Makefile for automating the handling of all of the steps described in the guide. The only user customizations that should be necessary are the lists of dependent files. Tab characters are significant in Makefiles, and are not equivalent to spaces, so do not copy their contents via cut-and-paste from a Web browser window: download the file instead!
The subdirectory bibtex contains all of the public BibTeX style files long available at the University of Utah Mathematics Department that are not also in recent TeX Live distributions. However, you are strongly advised to stick with one of the basic four styles in original 1986 LaTeX if you are to avoid formatting disputes with the Thesis Office.
The three sample theses are: