The quality of journal articles relies heavily on the quality of the peer review that those articles receive, and Jennifer Raff at Violent Metaphors notes that how to review a manuscript is not always explicitly taught to graduate students.
At her blog she pulls together a list of guidelines and tips to help young scientists review a manuscript. There are, she notes, a number of ethical considerations to keep in mind, including being honest about whether you have enough expertise in that field to be a reviewer, not reviewing a paper from authors that you either strongly like or dislike, and respecting the confidentially clause.
To "critically, but fairly" review a paper, Raff suggests taking notes as you go, and asking yourself a number a questions as you do so. For instance, ask whether the paper is original and interesting, whether it uses proper controls, and whether how the authors interpret their results is reasonable, among others.
"Draft your response only after you've read the entirety of the submission (including Supplementary Online Information) several times!" she says. "Avoid being unnecessarily harsh or abusive; your criticism should be constructive in tone."