The elsarticle document class uses a comma to separate multiple authors; if you are using this document class, then I would advise you not to change the pre-stablished formatting; it was designed specifically to satisfy the requirements of Elsevier. However, if you decide to change the template, then you will need a redefinition of the internal \@author command, as shown below (warning: will use "and" between all authors):
\documentclass[final,times,1p,leqno,11pt]{elsarticle}
\makeatletter
\def\@author#1{\g@addto@macro\elsauthors{\normalsize%
\def\baselinestretch{1}%
\upshape\authorsep#1\unskip\textsuperscript{%
\ifx\@fnmark\@empty\else\unskip\sep\@fnmark\let\sep=,\fi
\ifx\@corref\@empty\else\unskip\sep\@corref\let\sep=,\fi
}%
\def\authorsep{\space and\space}%
\global\let\@fnmark\@empty
\global\let\@corref\@empty
\global\let\sep\@empty}%
\@eadauthor={#1}
}
\makeatother
\title{The Title}
\author{The First Author}
\author{The Second Author}
\begin{document}
\maketitle
\end{document}
