For two independent side-by-side figures, you can use two minipages inside a figure enviroment; for two subfigures, I would recommend the subcaption package with its subfigure environment; here's an example showing both approaches:
\documentclass{article}
\usepackage[demo]{graphicx}
\usepackage{caption}
\usepackage{subcaption}
\begin{document}
\begin{figure}
\centering
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=.4\linewidth]{image1}
\caption{A subfigure}
\label{fig:sub1}
\end{subfigure}%
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=.4\linewidth]{image1}
\caption{A subfigure}
\label{fig:sub2}
\end{subfigure}
\caption{A figure with two subfigures}
\label{fig:test}
\end{figure}
\begin{figure}
\centering
\begin{minipage}{.5\textwidth}
\centering
\includegraphics[width=.4\linewidth]{image1}
\captionof{figure}{A figure}
\label{fig:test1}
\end{minipage}%
\begin{minipage}{.5\textwidth}
\centering
\includegraphics[width=.4\linewidth]{image1}
\captionof{figure}{Another figure}
\label{fig:test2}
\end{minipage}
\end{figure}
\end{document}
Refer to the link at the beginning for details posted,