The peer review is always the trickiest part of the writing process. A lot of people don't use the resource of peer review's seriously and therefore don't realize it's full potential. A peer review is one of the best things you can do in your writing process. When you sit down to write something, whether it takes 1 hour, 1 week, or 1 month, you become consumed in it; you start to not notice when you write something awkwardly or maybe you just don't know how to say what you want to say. That's where the peer reviews become really helpful.
Once you complete your REALLY rough draft, it's time for a peer review. Now this draft should not be great. It should be a narrative of ideas describing what you want to say in your paper.
I always recommend having two separate people peer edit for you: the first should be in your class/ familiar with the material, and the second should be someone who knows nothing more than common sense about the subject and is not in your class. The reason your first peer editor should be in your class is because this draft of your paper is just your ideas. If you have someone who is in your class and familiar with the material, they can interpret what your trying to say and may be able to help word your thoughts better.
After writing your second or final draft have someone who is not in your class review it. This can ensure that you are getting your message across clearly, since the whole point of a paper is to introduce and explain a point to even someone who knows nothing on the subject. You want them to pick up your paper and completely understand your thought process when they get to the end. They will also be able to point out more simple and easily missed errors or grammatically incorrect sentences that you may not have noticed while writing the paper.
Always remember to take peer recommendations with a grain of salt. You may encounter a peer editor who has no sense of grammar, or who tries to correct a statement you've made that you know is correct. It may be helpful to have multiple people revise the same draft to avoid poor peer edits.