According to me reviewing of manuscript allow me to learn by comparing my own reviews with other reviews of the same field or article.
To review paper I follow main steps used generally by most of reviewers :
1-I accept an invitation to review an article if the topic is of interest to me, if it is within my expertise, and if I can commit the time.
2- I do my first reading
3- I analysis the experimental design, methods, results, and bases for conclusions, and particularly to note what the authors think is important in their work
4- I check the literature, consult a colleague, or do some hard thinking, identify errors of the science.
5- I verify contradiction, unwarranted conclusion or attribution of causation, inappropriate extrapolation, circular reasoning, pursuit of a trivial question and violations of abstruse principles. Also ethical consideration is verified as uncovered inappropriate treatment of human or animal subjects.
Basically, the manuscript should be reviewed for originality, design and methodology, writing style, data analysis, contribution to the field and novelty of results.
Reviewing a manuscript needs careful and close observation by the reviewer on different levels: language, style, organization of ideas, relevance of information, cortect ciration, use of references, methods of analysis, etc. Reviewers have to be neutral and fair in writing notes and making decisions.
When I review a manuscript, I begin by checking the APA style of the reference list. (This is the style guide in my discipline). My experience is that manuscripts that make a solid effort to comply with the details of reference list style guidelines tend to be crafted with more care and are a more serious effort to get published.
So very many manuscripts appear to be slapped together to satisfy some kind of expectation that something be submitted - regardless of the quality.
After reviewing the reference list, I then read through the manuscript in detail, noting each source cited as well as every question that is raised by this first reading. Often, this level of reading leads quickly to a rejection when there is a lack of congruence between the research hypothesis, methodology, or statistical analyses.
When a manuscript has publication potential, I often find that I need to step back a bit from the details to consider the overall conceptual argument. What review notes can I offer that will significantly improve the manuscript? Sometimes I have to set the manuscript aside for a day or two to think about it.
Finally, I write my review and submit it to the journal. A rejection usually takes less than 2 hours. An acceptance (with revisions) is twice as long.