I wouldn't bother, as they will probably use the LaTeX source for their typesetting. But if you really want to comply, here is a way:
\documentclass[authoryear,preprint,review,12pt]{elsarticle}
\journal{Journal of Parallel and Distributed Computing}
%% Code added to comply with the requirement that the
%% abstract is on the second page together with the keywords.
%% Remove up to the <end of patch> line for removing the patch.
\usepackage{etoolbox}
\patchcmd{\pprintMaketitle}
{\ifvoid\absbox\else\unvbox\absbox\par\vskip10pt\fi}
{\ifvoid\absbox\else\clearpage\unvbox\absbox\par\vskip30pt\fi}
{}{}
\patchcmd{\pprintMaketitle}
{\hrule\vskip12pt}
{}
{}{}
\patchcmd{\pprintMaketitle}
{\hrule\vskip12pt}
{}
{}{}
\appto{\pprintMaketitle}{\clearpage}
%% <end of patch>
\begin{document}
\begin{frontmatter}
\title{Title of the Paper {\Large (Regular Submission)}}
\author{Author 1}
\ead{author1@domain.com}
\author{Author 2}
\ead{author2@domain.com}
\address{Address}
\begin{abstract}
Text of abstract
\end{abstract}
\begin{keyword}
%% keywords here, in the form: keyword \sep keyword
\end{keyword}
\end{frontmatter}
% \linenumbers
%% main text
\section{Section 1}
\end{document}
I've also removed the now useless horizontal rules and spaced out a bit more the keywords from the abstract.
No one wanted to answer my question, there were just some comments debating whether documentation is adequate or not (notably without any links to support claims of adequate documentation). So I will try to answer it myself.
The first trick is to use a titlepage, where you can design the first page of the document regardless of how the rest looks. I ended up using this to just put some header picture and text, title, author, date, with some nice formatting. So I diverged from my original intention to make a copy of the Elsevier article, which has both abstract and start of the article text on the front page. But by using the titlepage tag, I don't need to learn how to write a document class, because I can just use the standard article class (probably works with report class too I guess).
\begin{titlepage}
... code for first page ...
\end{titlepage}
The second trick is to use minipages. It can be seen in the "header" example I linked in the question, but can also be used to set a list of authors to the left and then the abstract to the right of that. Here is an example to put two authors spaced out left and right side of the page using minipages:
\begin{minipage}[t]{0.5\textwidth}
\begin{flushleft}
\large
\emph{Author:}
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Author
Mr.~Dan-Erik \textsc{Lindberg}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Author
\end{flushleft}
\end{minipage}
%
\begin{minipage}[t]{0.3\textwidth}
\begin{flushright}
\large
\emph{Co-author:}
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Co-author
Dr. Firstname \textsc{Surname}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Co-author
\end{flushright}
\end{minipage}
These few things should be enough to put together any layout. But there are some additional things you might want to look at. Such as, the package xcolor with the colorbox and parbox combination, for an easy way to put boxes with background color and white text (for example) or similar layout things.
Since I ended up in an entirely different place than where I started, I don't really see a reason to post my final solution here, because it isn't an answer to the question, but the above tips should get anyone started to produce something similar to Elsevier et al.
Best Answer
Looking at the source the only way I can see to get a sensible output from two column in preprint style is to put the
frontmatterinto the optional argument of an explicit\twocolumnOr you can correct the width locally within a one-column frontmatter: