You should address the following three areas when editing another student's paper:
First, correct any syntax errors: misspellings, grammatical errors, omitted or misplaced words, and punctuation errors. A list of common errors can be found on the class webpage.
Style suggestions are a bit more subjective, but that doesn't meant they are less important. Style suggestions include rewording to make a phrase clearer or less awkward, breaking a long, wordy sentence into two separate sentences, and suggesting alternative (better) word choices. The goal is clear, simple, elegant wording. Sometimes academic papers get wordy and complicated, in part because there is a perception that they are "supposed" to sound that way, or because the writer has gotten highly involved in the topic, and has forgotten take a step back to look at the "big picture."
III. Content and Organization
Content is the message of the paper. As you edit for content, you should examine whether statements or arguments made by the author are logical and well-supported. Mark gaps or holes in an argument, unsubstantiated claims, and sweeping assumptions. You may suggest including additional information that has been omitted and that you think is relevant. You may also have suggestions for additional support from journal articles or other sources, or you may think an article that has been cited is not appropriate as supporting information. Finally, you also want to look at the overall organization of the paper. Does it have direction? Can you easily identify the main points? Is it clear at the end of the paper what the "take-home" message is? Does this paper actually say anything?
Writing your comments
Syntax errors and some style errors can be made directly on the text by crossing things out and writing things in. However, sometimes it might be better to move to the margins to make your corrections. Try to write legibly! If you use symbols or abbreviations (e.g. "awk" for awkward, "wc" for word choice), define them somewhere. Make sure you don't abbreviate so much that your suggestion is unclear. For content and organization suggestions, you may have to write your comments at the end of the paper, or on the back, or even on a separate sheet of paper. Be clear what your suggestions refer to, either by mentioning paragraph and line numbers, or numbering your comments and inserting corresponding numbers at the applicable points in the paper. You may also want to include global suggestions or summary statements that refer to the whole paper rather than any one part.
Tone of comments
Keep in mind that your comments are suggestions to the author. He or she is not obligated to take them, and thus, the more your comments are seen as constructive and not simply evaluative, the more helpful they will be. In terms of the points you receive for being a peer editor, simply being harsh or verbose will not be rewarded; incisive and well thought-out suggestions will. Editing may also include comments about what the author has done well, or particularly strong aspects of the paper. At all times, keep in mind that your job is to help the author write a better paper--this goal should help direct the tone and content of your comments.