The first question we need to consider is, "why bother with peer review at all?" The short answer that peer review is at the foundation of all you know and is the bedrock of the scientific process. (1:27)
So, how do you approach a review, and, more importantly, what do you write?
The approach is that you want to read and fully understand the work being reported in the paper, and point out the logical and technical shortcomings of the work along with the confusing or irregular points in the text, tables and figures.
As to writing, there is a standard formula.
Begin with a blank document in your favorite word processor. Begin your first paragraph with the following sentence prototype:
In the paper <<insert title here>><<insert author(s) here>> demonstrated <<insert main theme here>>. Continue through the first paragraph recapitulating the work presented and the meaning of those results. The first paragraph is written to demonstrate that you have read, and more importantly understood, the paper. If you can demonstrate understanding, authors will be more receptive to what you are about to write....
In the second (and subsequent, if necessary) paragraph, begin pointing out the errors and irregularities in the work and paper. Write about each element in a separate paragraph (hint: when you get referee comments about your papers, the shorter they are the better). Identify the element in question and give your reason(s) for concern with evidence from other work. Generally your criticism paragraphs are ordered from the most serious scientific problems to the very minor grammar and style concerns.
In the final summary paragraph of your review, be sure to make a direct recommendation to the editor from one of the following:
The paper is acceptable for publication
The paper is acceptable for publication with revision
The paper is not acceptable for publication
And that's how to write a peer review comments. Easy.
But I know what you're thinking ... I'm not an expert on the topics I have to read about in my peer's papers, and the papers we have are reviews, there aren't any experiments to evaluate.
True. You will write your review more on the logic, the organization, the clarity, the style and the mechanics of the papers you read. You do not need to fact check every assertion by reading every paper cited. We are writing reviews to practice the method and primarily to offer early assistance to our peers.
The large question you should think about as you read your papers is, "what have I learned and did I have any trouble understanding what was presented?" The answers to these questions will help guide your reveiw and give maximum feedback for your peers.
And remember peer review is anonymous, do not include your identity in the review, but be warned that the community is small so your style and focus may give away strong clues as to your identity.