I'm using WinEdit 9.0 along with MikeTex 2.9.
My document preamble reads as follows:
% ----------------------------------------------------------------
% Article Class (This is a LaTeX2e document) ********************
% ----------------------------------------------------------------
\documentclass[12pt]{article}
\usepackage[english]{babel}
\usepackage{amsmath,amsthm}
\usepackage{amsfonts}
% THEOREMS -------------------------------------------------------
\newtheorem{thm}{Theorem}[section]
\newtheorem{cor}[thm]{Corollary}
\newtheorem{lem}[thm]{Lemma}
\newtheorem{prop}[thm]{Proposition}
\theoremstyle{definition}
\newtheorem{defn}[thm]{Definition}
\theoremstyle{remark}
\newtheorem{rem}[thm]{Remark}
\numberwithin{equation}{section}
% ----------------------------------------------------------------
\begin{document}
...
How do I use the \begin{flushleft} \end{flushleft} commands to cause the content of a \begin{eqnarray*} \end{eqnarray*} to start from the left margin in the .pdf output document, instead of (what it seems to me) its default setting of being centered?

\documentclass{...}, the required\usepackage's,\begin{document}, and\end{document}. That may seem tedious to you, but think of the extra work it represents for TeX.SX users willing to give you a hand. Help them help you: remove that one hurdle between you and a solution to your problem. – erik Apr 11 '15 at 16:09eqnarray*(it's outdated), there are better ways (e.galign*etc fromamsmath).flushleftshould be replaced byraggedleftetc. And what erik said above ;-) – Apr 11 '15 at 16:09