It is important to note that as you receive an invitation to peer review, you should be sent a copy of the paper's abstract to help you decide whether you wish to do the review. It is ethical to respond to invitations promptly to prevent delays. At this stage it is really essential to declare any potential Conflict of Interest.
The review report structure varies between journals. Generally, an informal structure is followed, while, others have a more formal approach.
Basically, journals don't provide any specific criteria for reviews beyond asking for your 'analysis of merits'. If this is the case, then you may wish to familiarize yourself with examples of other reviews done for the journal, which the editor should be able to provide or, gradually as soon as you gain experience, you can rely on your own evolving style.
Other journals require a more formal approach. Sometimes even you may be asked to address specific questions in your review via a questionnaire. You might even be wished to rate the manuscript on various attributes using a scorecard. Basically, you are not able to observe these until you log in to submit your review. So soon after accepting to review the work, it's really worth checking for any journal-specific guidelines and requirements. If you receive formal guidelines, it is suggested get them to direct the structure of your review.
Even if specifically, the reporting format is provided by the journal it seems important to note that you are expected to compile comments to authors and possibly confidential ones to editors only.
It is important to move along the invitation to review. As you'll have received the article abstract, you should already understand the aims, key data and conclusions of the manuscript. If you don't, make a note now that you are required to feedback on how to specifically improve those sections.
You are suggested the first read-through that is skim-read. It is important to note that you will be assisted if you form an initial impression of the paper and get a sense of whether your eventual recommendation will be to accept or reject the paper.
Keep the following question in your mind - they'll help you form your overall impression:
While reading the whole paper, it is essential to make the right choice of what to read first can save time by flagging major problems early on. Editors say, "Significant recommendations for remedying flaws are VERY welcome."
In any case experimental design features prominently exist in the paper, then you should first of all check that the methodology is sound - if not, this is likely to be a major flaw.
Should present coherent analysis, statistical relevance, and contextualize findings within existing literature.
Must reflect aims and be supported strictly by evidence.
Check accuracy, adequacy, balance, and avoidance of excessive self-citation.
Report suspected plagiarism or ethical concerns confidentially to editors.
Be constructive, objective, respectful, and precise. Provide actionable feedback with page and line references.