Reviewing really comes from experience, and that's partly why it is limited to users who have reached enough reputation. I don't think there are any hard and fast rules written down anywhere on what to look for because the expectation is that users performing the reviews have established themselves in the community and know what is expected, or not acceptable, on the site.
That said, we do tend to have some tricky rules if you haven't been really active on meta. Resource/book recommendations, homework, computational, engineering, and experimental questions all have very specific policies that have many subtleties.
Aside from those, the usual correction of grammar, formatting, MathJax, removing greetings/thanks/superfluous information, and proper tagging are always safe and a good way for new reviewers to help new users.