By default, section-level numbering is defined in report.cls as
\renewcommand \thesection {\thechapter.\@arabic\c@section}
which prepends the section number with \thechapter.. The other lower-level sectioning commands follow a similar hierarchy. As such, you could just use the report document class and remove the \chapter numbering from (all) the lower-level sectioning commands (like \section and \subsection) using
\renewcommand{\thesection}{\arabic{section}}
Other chapter-related may also require redefinition, although this is not technically necessary. For example, \theequation, \thefigure and \thetable all condition on the value of the chapter counter, prepending it with \thechapter. only if \c@chapter>\z@ (chapter counter is greater than zero, which is only incremented from 0 at the first sign of \chapter). Regardless and for completeness:
\renewcommand{\theequation}{\arabic{equation}}
\renewcommand{\thefigure}{\arabic{figure}}
\renewcommand{\thetable}{\arabic{table}}
Here's a minimal example (without anything special) that just shows the sectioning structure:

\documentclass{report}
\usepackage{lipsum}% http://ctan.org/pkg/lipsum
\author{A.\ Nonymous} \title{My title} \date{\today}
\renewcommand{\thesection}{\arabic{section}}%
\begin{document}
\maketitle
\tableofcontents
\section{First section} \lipsum[1]
\subsection{First subection} \lipsum[2]
\subsection{Second subsection} \lipsum[3]
\subsubsection{First subsubsection} \lipsum[4]
\section{Second section} \lipsum[5]
\end{document}