When should a graduate student accept a peer-review request?
Writing peer reviews is a vital part of academic life and you should eventually partake in such service to the community. In order to write a good review, you need
- time to actually read the manuscript and write the review;
- sufficient scientific expertise in the relevant field;
- some idea of what constitutes a good review;
- confidence in your own judgement and in your critique of (potentially much more senior) authors.
Reviewing is always much easier and pleasant if the manuscript is good. When there are problems with the manuscript, that's where it becomes tricky (unfortunately, many submitted manuscripts fall in the second category).
You should definitely discuss this with your supervisor.
Grad students can certainly review papers. Most likely there will be something like 3 reviews, and the others will be faculty or other more experienced reviewers. If you think you know the area, go for it! Need to pay forward the efforts of those reviewing your papers, after all.