\centering
% figure1
\begin{minipage}{.48\textwidth}
\centering
\includegraphics[width=\linewidth]{figure1.png}
\caption{caption1} \label{fig:figure1}
\end{minipage}
\hfill
% figure2
\begin{minipage}{.48\textwidth}
\centering
\includegraphics[width=\linewidth]{figure2.png}
\caption{caption2} \label{fig:figure2}
\end{minipage}
\end{figure}
*\textwidth : the global width of the textarea
**\linewidth : the width with respect to the list (or the column width of the each minipages in this case)
Also, by using a package "subcaption"
you can have a subcaption for each panel, and a main caption.
\usepackage{subcaption}
\begin{figure}[h]
\centering
% figure1
\begin{minipage}{.48\textwidth}
\centering
\includegraphics[width=\linewidth]{figure1.png}
\subcaption{caption1} \label{fig:figure1} % figure index will be (a)
\end{minipage}
\hfill
% figure2
\begin{minipage}{.48\textwidth}
\centering
\includegraphics[width=\linewidth]{figure2.png}
\subcaption{caption2} \label{fig:figure2} % figure index will be (b)
\end{minipage}
\caption{main-caption} \label{main-label} % figure index will be a number
\end{figure}