As I've published more and more, I've been invited to become a reviewer for many conferences and journals. Some are by people I've met while presenting at conferences, but others come randomly in my inbox from people who have read my papers. There's something that seems weird about being an "expert reviewer" while still not completed my studies myself - but I've always accepted when I've had time to do them because I feel like it's good to volunteer back some time after other people have done the same work to review my papers.
Generally, I stick to accepting review requests for papers which are very closely related to my area of study. In the cases where I'm not sure of something, I ask for advice from other grad students in the areas I am lacking in expertise. I also usually give a comment to the editor letting them know I am just a PhD student, and to take my opinion with less weight than more qualified reviewers. That being said, I think I usually am thorough and give useful feedback to the authors' of papers I review.
Getting invited to review so often has also made me question the whole review and acceptance process. It would be nice if journals and conferences disclosed how many of the reviewers have PhDs - although I guess it wouldn't really tell much because I've also been handed papers by professors I work with and been told to review them and give them a report which I assume they use to submit the review themselves. In some respects it makes sense to have grad students review papers since they are often very connected to the current research, but I am still not confident about the process if it is possible for papers to be accepted without even being looked at by a real PhD. Maybe I just don't know enough about how it all works yet to know for sure. After all, there's always layers of editors and committees and everything else.
In any event, here's a couple of links about how to review a paper for any other grad students who find themselves in the same boat:
<a href="http://www.cs.ucsb.edu/~ebelding/courses/284/papers/ReviewingPapersStudentGuide.html" title="http://www.cs.ucsb.edu/~ebelding/courses/284/papers/ReviewingPapersStudentGuide.html">http://www.cs.ucsb.edu/~ebelding/courses/284/papers/ReviewingPapersStudentGuide.html</a>
<a href="http://www.raulpacheco.org/2013/06/the-ethics-of-academic-peer-review-some-tips-and-best-practices/" title="http://www.raulpacheco.org/2013/06/the-ethics-of-academic-peer-review-some-tips-and-best-practices/">http://www.raulpacheco.org/2013/06/the-ethics-of-academic-peer-review-some-tips-and-best-practices/</a>