Indent for first line
This is actually the default behavior in TeX. The amount of indenting can be controlled by setting the length \parindent.
\documentclass{article}
\setlength{\parindent}{20mm}
\begin{document}
A quite long sentence a quite long a sentence quite a long sentence a quite long sentence.
A quite long sentence a quite long a sentence quite a long sentence a quite long sentence.
\end{document}

Note that the indent only applies for normal paragraphs and not section headings etc. if you want these also to be indented (which I don’t recommend!) you must redefine them e.g. with titlesec package or when using KOMA-Script with \RedeclareSectionCommand.
Outdent for all lines except the first one
If you want all line except the first one you can use \parshape together with \everypar (must be used after \begin{document} or with \AtBeginDocument).
\documentclass{article}
\usepackage{showframe}
\setlength{\parindent}{0pt}
\AtBeginDocument{
\everypar{%
\parshape 2
0pt \textwidth
-2em \dimexpr\textwidth+2em\relax
}
}
\begin{document}
A quite long sentence a quite long a sentence quite a long sentence a quite long sentence.
A quite long sentence a quite long a sentence quite a long sentence a quite long sentence.
A quite long sentence a quite long a sentence quite a long sentence a quite long sentence.
A quite long sentence a quite long a sentence quite a long sentence a quite long sentence.
\end{document}

However it looks really strange and is unusual – don’t use it ;-)
Mor about \parshape: Opposite of \parindent
Edit: To preserve this setting at a \section you must re-apply it afterwards, because \everypar is re-setted. I use \ReneowDocumentCommand from the sparse package.
\documentclass{article}
\usepackage{showframe}
\setlength{\parindent}{0pt}
\newcommand{\activateoutdenting}{%
\everypar{%
\parshape 2
0pt \textwidth
-2em \dimexpr\textwidth+2em\relax
}
}
\AtBeginDocument{\activateoutdenting}
\usepackage{xparse}
\let\origsection\section
\RenewDocumentCommand{\section}{ s o m }{%
\IfBooleanTF{#1}{%
\IfValueTF{#2}{%
Impossible case!%
}{%
\origsection*{#3}%
}
}{%
\IfValueTF{#2}{%
\origsection[#2]{#3}%
}{%
\origsection{#3}%
}
}
\activateoutdenting
}
\begin{document}
A quite long sentence a quite long a sentence quite a long sentence a quite long sentence.
A quite long sentence a quite long a sentence quite a long sentence a quite long sentence.
A quite long sentence a quite long a sentence quite a long sentence a quite long sentence.
A quite long sentence a quite long a sentence quite a long sentence a quite long sentence.
\section{Test}
A quite long sentence a quite long a sentence quite a long sentence a quite long sentence.
\end{document}
Note that this hast to be done for other section headings too and this is no robust implementation. I repeat myself but: Why would you do this? It looks awful …
\documentclass{...}and ending with\end{document}. – Holene Mar 30 '16 at 15:15\newenvironment{outdent}% {\begin{list}{}% {\listparindent=3em\itemindent=\listparindent\leftmargin=-3em}% \item[]}% {\end{list}}
– ChokuRei Mar 30 '16 at 17:12