If you use the preprint
style, here's a patch:
\documentclass[preprint, authoryear]{elsarticle}
\usepackage{etoolbox}
% patch `\maketitle` to accommodate the new information, printed after the keywords
\patchcmd{\pprintMaketitle}
{\fi\hrule}% the second rule
{\fi\ifvoid\extrainfobox\else\unvbox\extrainfobox\par\vskip10pt\fi\hrule}
{}{}
% an environment for the new information
\newenvironment{extrainfo}
{\global\setbox\extrainfobox=\vbox\bgroup\parindent=0pt }
{\egroup}
\newsavebox\extrainfobox
\bibliographystyle{annesstyle}
\begin{document}
\begin{frontmatter}
\title{title}
\author[firstaddress]{Aaddress}
\author[secondaddress]{address}
\author[thirdaddress]{Haddress}
\author[thirdaddress]{address}
\author[thirdaddress]{address}
\author[thirdaddress,firstaddress]{address}
\address{Address for correspondance:}
\address[firstaddress]{address}
\address[secondaddress]{address}
\begin{abstract}abstract\end{abstract}
\begin{keyword}keywords\end{keyword}
\begin{extrainfo}
Number of pages: ;\\
Number of figures: ;\\
Number of tables: ;\\
Number of words in the abstract: ;\\
Introduction: ;\\
discussion: ;\\
Total number of words in the text: ;\\
Conflict of interest:
\end{extrainfo}
\end{frontmatter}
\section{References}
\bibliography{mybib}
\end{document}

Here's the way to have the extra information before the abstract:
\documentclass[preprint, authoryear]{elsarticle}
\usepackage{etoolbox}
\patchcmd{\pprintMaketitle}
{\hrule\vskip12pt}% the second rule
{\hrule\vskip12pt\ifvoid\extrainfobox\else\unvbox\extrainfobox\par\vskip12pt\fi}
{}{}
\newenvironment{extrainfo}
{\global\setbox\extrainfobox=\vbox\bgroup\parindent=0pt }
{\egroup}
\newsavebox\extrainfobox
\bibliographystyle{annesstyle}
\begin{document}
\begin{frontmatter}
\title{title}
\author[firstaddress]{Aaddress}
\author[secondaddress]{address}
\author[thirdaddress]{Haddress}
\author[thirdaddress]{address}
\author[thirdaddress]{address}
\author[thirdaddress,firstaddress]{address}
\address{Address for correspondance:}
\address[firstaddress]{address}
\address[secondaddress]{address}
\begin{abstract}abstract\end{abstract}
\begin{keyword}keywords\end{keyword}
\begin{extrainfo}
Number of pages: ;\\
Number of figures: ;\\
Number of tables: ;\\
Number of words in the abstract: ;\\
Introduction: ;\\
discussion: ;\\
Total number of words in the text: ;\\
Conflict of interest:
\end{extrainfo}
\end{frontmatter}
\section{References}
\bibliography{mybib}
\end{document}

The text in the second arguments of \patchcmd
is the code that we want to replace in the definition of \pprintMaketitle
with the code contained in the third argument. It's easier than copying the entire definition and modifying it.