LaTeX.org

Ok, I found the problem. But now when I do:
\begin{figure}
\includegraphics{Figure1.png}
\end{figure}

The image will only show up at the top of the page it ends up on.

I can generate the pdf file. I can see it with Acrobat Reader. So I think that, in your case, there are many compilation errors, pdfLaTeX doesn't build the pdf and so you cannot open or see it. Am I right?

Yep

Ok, here's where the figure would go:
\documentclass[11pt,letterpaper]{paper}
\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{makeidx}
\usepackage{hyperref}
\usepackage{graphicx}
\author{Cory Wilson}
\begin{document}
\begin{enumerate}
\begin ...

I put "\usepackage{graphics}" and "\usepackage{graphicx}" in the preamble, but now when I try to view the pdf, it gives me this message:

Adobe reader could not open the file "trilinability.pdf" because it is either not a supported file type or because the file has been damaged (for example, it was ...

I've tried it in TexnicCenter, too, but the image won't output. Here's the log output:

This is pdfeTeX, Version 3.141592-1.30.6-2.2 (MiKTeX 2.5) (preloaded format=pdflatex 2007.2.1) 13 DEC 2007 03:47
entering extended mode
**trilinability.tex
(trilinability.tex
LaTeX2e <2005/12/01>
Babel <v3.8g ...