Students need to see examples of properly executed peer editing. If you merely ask them to switch papers and hand them a critique sheet, the students will usually make shallow edits and leave few comments. As a result, you should describe the peer editing process and clearly outline your expectations. Pass out a copy of a paper that has gone through peer editing along with the completed critique sheet. Explain what the peer editor did well during the review so the students can emulate their review process when they have another student's paper to critique.
Guide the students through their first peer review. Students should read the paper first for quality of content and to assess how well the student met the assignment criteria. Explain what they should look for as they read the paper and describe how they should write their comments on the critique sheet. Then, take the students point-by-point through the grammatical criteria, explaining what they should look for as you address each criterion on the critique sheet. Even college students forget terminology like comma splice or split infinitive, so provide examples of these errors to guide them.
After the students have completed their peer editing, grade their efforts. Students work harder to provide a thorough edit if they know they will be evaluated. The students will not catch every error or find every problematic passage in the paper, but they should catch obvious problems with logic as well as major errors. Grade them for their efforts, as well as the depth of their written responses on the student's work. They shouldn't just write "spelling errors," for example. They should explain any patterns of spelling errors as well as provide examples of these errors.
Without feedback on their editing, students can become complacent and start leaving general, shallow comments that aren't helpful to the writer. To remedy this, share particularly well-considered edits to the class. Remove the name of the student whose paper was critiqued to avoid embarrassment. Instead, focus on the editor and what she did well. Most students enjoy being praised, and showing good examples of peer editing keeps the students working hard to provide quality feedback.