Peer reviewing is a pivotal part of scientific publication process, and it's meant to ensure that the data collected by researchers is properly scrutinized to find majour flaws or incoherences in the theory or methodology behind it. Nonetheless, nowaday, scientists receive little -if any- training in this, and most of the ability to analyze and review a scientific paper comes from raw experience.
Mathew Stiller-Reeve wrote this quite useful vademecum that's meant to list all the majour elements that a reviewer should address as he's peer-reviewing a scientific paper.
A flow chart, that summarizes the entire process, as meant by the author, is available here
Surce: Nature Website