\documentclass[12pt]{article}
\usepackage{fixltx2e}%% the official fixes for LaTeX2e
\usepackage[T1]{fontenc}
\usepackage[scaled=0.92]{helvet}
\usepackage{mathptmx}
\usepackage{courier}
\makeatletter
\def\verbatim@font{\small\normalfont\ttfamily}
\makeatother
\newenvironment{ParagraphLeftIndent}[1]{%
  \begin{list}{}{%
    \setlength\topsep{0pt}%
    \addtolength{\leftmargin}{#1}
    \setlength\parsep{0pt plus 1pt}%
  }
  \item[]
}
{\end{list}}
\begin{document}
\textbf{Standard enumeration}

\begin{enumerate}
\item First item

\begin{enumerate}
\item First subitem
\item Second subitem
\end{enumerate}
\item Second item

\begin{enumerate}
\item Second subitem

\begin{enumerate}
\item second subsubitem
\end{enumerate}
\end{enumerate}
\item third item
\end{enumerate}
New enumerationstyle with redefining the labels with the following
latex commands:

\begin{ParagraphLeftIndent}{-3cm}
{\small
\begin{verbatim}
\renewcommand\labelenumi{\arabic{enumi}.}
\renewcommand\labelenumii{\arabic{enumi}.\arabic{enumii}.}
\renewcommand\labelenumiii{\arabic{enumi}.\arabic{enumii}.\arabic{enumiii}.}
\end{verbatim}}
\end{ParagraphLeftIndent}

\renewcommand\labelenumi{\arabic{enumi}.} \renewcommand\labelenumii{\arabic{enumi}.\arabic{enumii}.}
\renewcommand\labelenumiii{\arabic{enumi}.\arabic{enumii}.\arabic{enumiii}.}


\begin{enumerate}
\item First item

\begin{enumerate}
\item First subitem
\item Second subitem
\end{enumerate}
\item Second item

\begin{enumerate}
\item Second subitem

\begin{enumerate}
\item second subsubitem
\end{enumerate}
\end{enumerate}
\item third item
\end{enumerate}
There are five different ways to define the labels

\begin{enumerate}
\item \verb/\renewcommand\labelenumi{\Alph{enumi}}/ gives A, B, C,... 
\item \verb/\renewcommand\labelenumi{\alph{numi}}/ gives a, b, c,... 
\item \verb/\renewcommand\labelenumii{\Roman{enumii}}/ gives I, II, III,...
\item \verb/\renewcommand\labelenumii{\roman{enumii}}/ gives i, ii, iii,...
\item \verb/\renewcommand\labelenumiii{\roman{enumiii}}/ gives 1, 2, 3,
...
\end{enumerate}
The following example belongs to the definition of:

\verb/\renewcommand\labelenumi{\Alph{enumi}}/ 

\verb/\renewcommand\labelenumii{\Roman{enumii}}/

\verb/\renewcommand\labelenumiii{\roman{enumiii}}/

\verb/\renewcommand\labelenumiv{\arabic{enumiv}}/

\renewcommand\labelenumi{\Alph{enumi}} 
\renewcommand\labelenumii{\Roman{enumii}}
\renewcommand\labelenumiii{\roman{enumiii}}
\renewcommand\labelenumiv{\arabic{enumiv}}

\begin{enumerate}
\item First item with 

\begin{enumerate}
\item First subitem

\begin{enumerate}
\item First subsubitem

\begin{enumerate}
\item First subsubsubitem
\item Second subsubsubitem
\end{enumerate}
\end{enumerate}
\end{enumerate}
\item Second item

\begin{enumerate}
\item Second subitem

\begin{enumerate}
\item Second subsubitem

\begin{enumerate}
\item Second subsubsubitem
\item Third subsubsubitem\end{enumerate}
\end{enumerate}
\end{enumerate}
\end{enumerate}

\end{document}