How to have roman numerals at the beginning of the document?

If you are using the book class, start your document with \frontmatter. This changes the numbering to roman numerals. Then mark the main part of with \mainmatter. There are also \appendix (which changes the chapter numbering to uppercase letters) and \backmatter.

If you are using an article you can use:

\pagenumbering{Roman} 
\pagenumbering{arabic} 

\frontmatter and \mainmatter will suffice for different styles of page numbering, but not for roman numbering of introductory tables (which are quite uncommon). Assuming you have only one frontmatter chapter that includes tables, the following should do the trick:

\documentclass{book}

\begin{document}

\frontmatter

\begingroup
\renewcommand{\thetable}{\Roman{table}}

\chapter{foo}

Some text.

\begin{table}
\caption{bla}
\end{table}

\endgroup

\mainmatter

\chapter{bar}

Some text.

\begin{table}
\caption{blubb}
\end{table}

\end{document}

For report and similar classes, replace \frontmatter with \pagenumbering{Roman} and \mainmatter with \cleardoublepage\pagenumbering{arabic}.