This is easily accomplished using the wrapfig package if you're willing to specify the "number of lines" occupied by the block-quote. Here's a small example using dummy text created by lipsum:
\documentclass{article}
\usepackage{wrapfig}% http://ctan.org/pkg/wrapfig
\usepackage{lipsum}% http://ctan.org/pkg/lipsum
\begin{document}
\begin{wrapfigure}[25]{r}{.4\linewidth}
\fbox{\begin{minipage}{\dimexpr\linewidth-2\fboxrule-2\fboxsep}
\centering
``Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Proin ac tempus dui. Etiam non mattis neque. Maecenas tempor,
massa a luctus sollicitudin, elit massa auctor velit, eu mattis
lacus arcu nec est. Sed et lectus non tellus posuere consequat.
Donec congue lacinia urna a iaculis. Cras id nisl sed sapien
euismod rhoncus.
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Proin ac tempus dui. Etiam non mattis neque. Maecenas tempor,
massa a luctus sollicitudin, elit massa auctor velit, eu mattis
lacus arcu nec est. Sed et lectus non tellus posuere consequat.
Donec congue lacinia urna a iaculis. Cras id nisl sed sapien
euismod rhoncus.''
\end{minipage}}
\end{wrapfigure}
\lipsum[1-2]
\end{document}
Read the wrapfig documentation for more information on the environment specification for wrapfigure.
Note that this will be problematic if the block-quote spans beyond the page boundary.
Here is a proposal, using some low level commands. The text is typeset in a \vtop and its depth is used to place the opening quotes, while the closing quotes will be level with the top line (with some lowering due to size).
Thanks to Jake, I've been able to solve a mystery that bugged me, about a spacing that seems necessary and is due to the inner sep of TikZ nodes.
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[ngerman]{babel}
\usepackage{kpfonts}
\usepackage[svgnames]{xcolor}
\definecolor{framecolor}{named}{SteelBlue}
\colorlet{framebgcolor}{PowderBlue!50!White}
\definecolor{quotesignclr}{named}{LightSlateGrey}
\usepackage{changepage}
\usepackage{environ,graphicx}
\usepackage{tikz}
\usetikzlibrary{backgrounds}
\newcommand\sopeningquote{\scalebox{2}{\color{quotesignclr}\smash\quotedblbase}}
\newcommand\sclosingquote{\scalebox{2}{\color{quotesignclr}\smash\textquotedblleft}}
\makeatletter
\newsavebox\simplequestbox
\NewEnviron{simplequest}{%
\normalfont
\begin{adjustwidth}{3em}{3em}
\settowidth{\dimen@}{\sopeningquote\kern.4em\sclosingquote}%
\dimen@=\dimexpr\linewidth-\dimen@\relax
\setbox\simplequestbox=\vtop{
\@parboxrestore\itshape
\hsize=\dimexpr\dimen@-\pgfkeysvalueof{/pgf/inner xsep}*2\relax % thanks, Jake
\sbox\z@{\BODY}
\ifdim\wd\z@>\hsize
\noindent\BODY\par
\else
\box\z@
\fi
\xdef\simplequestpd{\the\prevdepth}
}
\begin{tikzpicture}
[background rectangle/.style={draw=framecolor,line width=0.2pt,
fill=framebgcolor,rounded corners}, show background rectangle,
inner frame xsep=-2pt,inner frame ysep=2pt]
\node {\mbox{%
\raisebox{\dimexpr-\dp\simplequestbox+\simplequestpd+.05ex}
[0pt][0pt]{\sopeningquote}%
\kern.2em
\box\simplequestbox
\kern.2em
\raisebox{-1.4ex}[0pt][0pt]{\sclosingquote}}};
\end{tikzpicture}
\end{adjustwidth}
}
\makeatother
\begin{document}
\begin{simplequest}
Dies hier ist ein Blindtext zum Testen von Textausgaben.
Wer diesen Text liest, ist selbst schuld.
\end{simplequest}
\begin{simplequest}
Dies hier ist ein Blindtext
\end{simplequest}
\Large
\begin{simplequest}
Dies hier ist ein Blindtext zum Testen von Textausgaben.
Wer diesen Text liest, ist selbst schuld.
\end{simplequest}
\end{document}
In the picture the similar quotes are: top mine, bottom yours.
A problem may arise in case the text consists of more than one paragraph and the first one is not long enough to fill a line. Should this case present itself in the document, the code might be changed like this:
\makeatletter
\newsavebox\simplequestbox
\NewEnviron{simplequest}[1][]{%
\normalfont
\begin{adjustwidth}{3em}{3em}
\settowidth{\dimen@}{\sopeningquote\kern.4em\sclosingquote}%
\dimen@=\dimexpr\linewidth-\dimen@\relax
\setbox\simplequestbox=\vtop{
\@parboxrestore\itshape
\hsize=\dimexpr\dimen@-\pgfkeysvalueof{/pgf/inner xsep}*2\relax % thanks, Jake
\if\relax\detokenize{#1}\relax
\sbox\z@{\BODY}
\ifdim\wd\z@>\hsize
\noindent\BODY\par
\else
\box\z@
\fi
\else
\sbox\z@{#1}
\hsize\wd\z@
\BODY\par
\fi
\xdef\simplequestpd{\the\prevdepth}
}
\begin{tikzpicture}
[background rectangle/.style={draw=framecolor,line width=0.2pt,
fill=framebgcolor,rounded corners}, show background rectangle,
inner frame xsep=-2pt,inner frame ysep=2pt]
\node {\mbox{%
\raisebox{\dimexpr-\dp\simplequestbox+\simplequestpd+.05ex}
[0pt][0pt]{\sopeningquote}%
\kern.2em
\box\simplequestbox
\kern.2em
\raisebox{-1.4ex}[0pt][0pt]{\sclosingquote}}};
\end{tikzpicture}
\end{adjustwidth}
}
\makeatother
The environment now has an optional argument, the first short line; here's an example:
\begin{simplequest}[Dies hier ist ein Blindtext.]
Dies hier ist ein Blindtext.
Wer diesen Text liest, ist selbst schuld.
\end{simplequest}
One could try getting only the first paragraph, but this might be error prone.
Best Answer
I wrote a package pullquote which allows to create circular as well as rectangular inserts.
See Two-column text with circular insert.