How to let enumeration start at (0) automatically?

I really don't know why one should want it. However, here's a solution with the enumitem package.

\documentclass{article}
\usepackage{enumitem}
\setlist[enumerate,1]{start=0} % only outer nesting level
\begin{document}
\begin{enumerate}
\item zero
\item one
  \begin{enumerate}
  \item a
  \item b
  \end{enumerate}
\item two
\end{enumerate}
\end{document}

You can also achieve it locally within the environment by using:

\setcounter{enumi}{-1} 

---

% arara: pdflatex: {synctex: yes, action: nonstopmode}
\documentclass{article}
\usepackage{enumerate} 
\usepackage[shortlabels]{enumitem} 
\begin{document}
\begin{enumerate}[\bf 1:,labelindent=10pt,leftmargin=*]
    \setcounter{enumi}{-1} 
\item zero
\item one
    \begin{enumerate}[\bf i:,labelindent=10pt,leftmargin=*] 
        \setcounter{enumii}{-1} 
        \item Nothing %testing with \roman, equivalent bold using \bf i
        \item one
        \item two
    \end{enumerate}
\item two
\end{enumerate}
\end{document}

Status:

SUCCESS