The package uses \section* (if \chapter is not available in the current document class) to format the title as an unnumbered section; you can patch (using, for example, the etoolbox package) the \thenomenclature command to use \section instead:
\documentclass{article}
\usepackage{nomencl}
\usepackage{etoolbox}
\makenomenclature
\makeatletter
\patchcmd{\thenomenclature}{\section*}{\section}{}{}
\makeatother
\begin{document}
\section{Introduction}
\nomenclature{A}{First one}
\nomenclature{B}{Second one}
\renewcommand{\nomname}{Abbreviations}
\printnomenclature
\section{Methods}
\end{document}

If you don't want to use additional packages, you'll need to make the change in the definition of \thenomenclature:
\documentclass{article}
\usepackage{nomencl}
\makenomenclature
\makeatletter
\def\thenomenclature{%
\@ifundefined{chapter}%
{
\section{\nomname}
\if@intoc\addcontentsline{toc}{section}{\nomname}\fi%
}%
{
\chapter{\nomname}
\if@intoc\addcontentsline{toc}{chapter}{\nomname}\fi%
}%
\nompreamble
\list{}{%
\labelwidth\nom@tempdim
\leftmargin\labelwidth
\advance\leftmargin\labelsep
\itemsep\nomitemsep
\let\makelabel\nomlabel}}
\makeatother
\begin{document}
\section{Introduction}
\nomenclature{A}{First one}
\nomenclature{B}{Second one}
\renewcommand{\nomname}{Abbreviations}
\printnomenclature
\section{Methods}
\end{document}