You can redefine the commands \thechapter, \thesection, \thesubsection which control the representation of the counters for chapters, sections, and subsections. The tocloft package can be then used to add the dots:
\documentclass{book}
\usepackage{tocloft}
\renewcommand\cftchapaftersnum{.}
\renewcommand\cftsecaftersnum{.}
\renewcommand\thechapter{\Roman{chapter}}
\renewcommand\thesection{\arabic{section}}
\renewcommand\thesubsection{(\alph{subsection})}
\begin{document}
\tableofcontents
\chapter{Test Chapter One}
\section{Test Section One}
\section{Test Section One}
\subsection{Test Subsection A}
\subsection{Test Subsection B}
\end{document}

Some other adjustments might be necessary, to prevent the chapter number from overlapping the title, and perhaps reducing the space between the section number and their titles; those adjustments can be something like:
\renewcommand\cftchapnumwidth{2.8em}
\renewcommand\cftsecnumwidth{2em}
\renewcommand\cftsecindent{3em}
\renewcommand\cftsubsecindent{5em}
chapters,sections, etc have the numbering scheme you've illustrated, or something else? For example, are yourchaptersactuallyCHAPTER 1,CHAPTER 2, etc, and you want them to look differently in thetoc? – cmhughes Dec 4 '11 at 23:31