You can use the wrapfigure environment (from wrapfig package). This environment creates a box making the main text wrap around it. You can specify the width of this box and its position (left, or right, as well as inside, or outside for double-sided documents). Moreover, this package natively include the specification of the overhanging width.
\begin{wrapfigure}{<position: l, r, i, or o>}[<overhang width>]{<total width of the wrapfigure>}
<content of the wraping figure>
\end{wrapfigure}

\documentclass{article}
\usepackage{lipsum}
\usepackage{wrapfig}
\usepackage{xcolor}
\begin{document}
\lipsum[1]
\begin{wrapfigure}{r}[.1\textwidth]{.4\textwidth}%
\textbf{\sffamily\Large\textcolor{blue!50!black}{``Good things might come to those who wait\dots''}}%
\end{wrapfigure}
\lipsum[2-3]
\end{document}

Original answer
This solution uses a parbox inside the wrapfigure, instead of the native overhang option of wrapfig. It is thus bulkier than the one suggested above in the edit.
This solution uses the wrapfigure environment (from wrapfig package). This package defines a floating box that the text wraps around. You can specify the width of this box and its position (left or right):
\begin{wrapfigure}{<position: R or L>}{<width of the wrapfigure>}
<content of the wraping figure>
\end{wrapfigure}
We fill this box with our quote. In order to make the text run across the margin, we put this text inside another box, a parbox, having a wider width than the one defined by the wrapfigure environment:
\parbox{<width of the box>}{<content of the box>}

\documentclass{article}
\usepackage{lipsum}
\usepackage{graphicx}
\usepackage{wrapfig}
\usepackage{xcolor}
\begin{document}
\lipsum[1]
\begin{wrapfigure}{R}{.2\textwidth}%
\parbox{.4\textwidth}{%
\textbf{\sffamily\Large\textcolor{blue!50!black}{``Good things might come to those who wait\dots''}}%
}%
\end{wrapfigure}
\lipsum[2-3]
\end{document}
MWE with explicit boxes:

\documentclass{article}
\usepackage{lipsum}
\usepackage{graphicx}
\usepackage{wrapfig}
\usepackage{showframe}
\begin{document}
\lipsum[1]
\begin{wrapfigure}{R}{.2\textwidth}%
\fbox{\parbox{.3\textwidth}{\textbf{\Large Good things might come to those who wait\dots}}}%
\end{wrapfigure}
\lipsum[2-3]
\end{document}
wrapfigureenvironment, instead of a picture as shown in how to text-wrap an image in latex. For what regards the margin overlapping, you could play around with real/fictional boxes dimensions. – ebosi Feb 02 '17 at 08:42\begin{figure} \begin{quotation} this is the quote \end{quotation} \end{figure}but I don't know how to place the figure environment to the side and over the margin... – Mario Feb 02 '17 at 08:45\textbf{<text>}macro, and\textcolor{<color>}{<text>}(from thexcolorpackage) to change text color.) – ebosi Feb 02 '17 at 10:33