this article on peer review was interesting and well written. You may know most of this by now but some of it may surprise you.
For the most part, scientists are not formally trained in how to do peer review, nor given continuing education in how to do it better. And they usually don't get direct feedback from the journals or other scientists about the quality of their peer reviewing. Instead, young scientists learn from their advisors—often when that advisor delegates, to the grad students, papers he or she had volunteered to review. Your peer-review education really depends on whether your advisor is good at it, and how much time they choose to spend training you.