You can use the titlesec package to customize the formatting for the sectional unit headings; the mdframed or the framed packages give you the possibility to get framed text; a little example:
\documentclass{article}
\usepackage{xcolor}
\usepackage{titlesec}
\usepackage{mdframed}
\usepackage{lipsum}% just to generate text for the example
\colorlet{mycolor}{gray!50}
\titleformat{\section}
{\normalfont\sffamily\Large\fontfamily{phv}\selectfont}
{\thesection.}{.5em}{}[\vspace{.2ex}\color{mycolor}\titlerule]
\newmdenv[linecolor=mycolor,skipabove=\topsep,skipbelow=\topsep,
leftmargin=-5pt,rightmargin=-5pt,
innerleftmargin=5pt,innerrightmargin=5pt]{mybox}
\begin{document}
\section*{Title}
\lipsum[2]
\begin{mybox}
\lipsum[2]
\end{mybox}
\end{document}

I wasn't sure about the desired width for the frame, so here's another option:
\documentclass{article}
\usepackage{xcolor}
\usepackage{titlesec}
\usepackage{mdframed}
\usepackage{lipsum}% just to generate text for the example
\colorlet{mycolor}{gray!50}
\titleformat{\section}
{\normalfont\sffamily\Large\fontfamily{phv}\selectfont}
{\thesection.}{.5em}{}[\vspace{.2ex}\color{mycolor}\titlerule]
\newmdenv[linecolor=mycolor,skipabove=\topsep,skipbelow=\topsep]{mybox}
\begin{document}
\section*{Title}
\lipsum[2]
\begin{mybox}
\lipsum[2]
\end{mybox}
\end{document}

\section? Or should it just be a title that is bold with a horizontal rule below it. What about the paragraph box: should it be breakable across the page boundary or not? – Werner Oct 23 '12 at 17:01