You can use the \caption* command provided by the caption package to typeset information
without label and without entry in the list of figures (tables). A little example assuming you are using the floating figure environment:
\documentclass{article}
\usepackage[demo]{graphicx}% demo option just for the example
\usepackage{caption}
\begin{document}
\begin{figure}
\centering
\caption{A test figure}
\label{fig:test}
\includegraphics{name}
\caption*{Source: some source}
\end{figure}
\end{document}

Of course, you can also simply write the source text:
\documentclass{article}
\usepackage[demo]{graphicx}% demo option just for the example
\begin{document}
\begin{figure}
\centering
\caption{A test figure}
\label{fig:test}
\includegraphics{name}\par
Source: some source
\end{figure}
\end{document}