The general idea behind this practice is that writing is a social process, involving both writers and readers, and one of the most effective ways by which writers can improve their work is to get feedback from readers and revise with that feedback in mind. 

Some important points:

• First, a practical matter:  be sure to print out a copy of the essay that you are commenting on before class, so that you will have it before you. 
• Read the whole piece before class, at least once, preferably more than once.  Then read it again in class, collectively, with someone reading it aloud while others follow along.  Don’t be in too much of a hurry.  Be generous to the writer, but if something doesn’t make sense in the text, don’t ‘fill in the blank’ and assume you know what the author was trying to say.  You are obliged to tell the author about incoherencies and problems in the argument.  Reading aloud can make it easier to spot such issues.
• You might want to write some notes on your reading of the piece before class, and you will certainly want to write down any thoughts you have about it from the class critiquing session.  You are responsible for posting a coherent commentary to the piece of at least 150 words on the blog.
• Be sure when writing your commentary to make constructive critical comments in addition to pointing out aspects of the writing that were in your view effective.  Simply cheerleading for your fellow students might make them (and you) feel good, but it will not help anybody to become a better writer.
• Be as concrete as possible in your comments.  This is a concrete comment: “Consider omitting or moving paragraph 2.  The theme it takes up seems out of place at that point in the essay, and it makes murkier what is otherwise a very fine introduction to the argument.”  Here are some comments that aren’t very concrete: “Great job!” or “Lacks focus!”
• Your comments should be detailed and substantive.  In no case should a commentary on a fellow classmate’s text be fewer than 150 words.
• Authors should take notes on the commentary they receive from others, the better to absorb its content through active reflection.
• Remember overall to be friendly about this and to try not to get adversarial or defensive (this last point applies especially to the authors).  No writing is perfect in its first incarnation/draft form; in fact, no writing is perfect even after many, many revisions.  The best writers talk about their desire to go back and revise even brilliant books they have written.  The whole idea here is that the crafting of effective arguments in writing is a complex process that takes a lot of time and effort and that can be greatly aided by a community of readers that actively aids the writers in the process of refining and revising an argument.  So, don’t feel personally attacked if someone says your argument is confusing.  Ultimately, the intent is to help you make a more effective argument.