I recently had the chance to observe a session with a student whose first language is nnot English, but I wouldn't go so far as to say that she's an ESL student, as her accent was thin, and she kept up in conversation. I have to admit, however, that as the session continued, the language barrier did become a bit of a focal point.
Upon arrivial, the student said that she wanted to "correct" her paper, and when pressed, admitted that correcting punctuation and vocabulary was her goal for the session.The tutor began to read through the paper and made small notes on the page. Meanwhile, the writer sat quietly and fiddled with various papers and looked generally disinterested. Upon noting this behavior, my initial thought was that this student, like others I've seen, had no desire to be at the writing center and only there to appease her instructor. Looking back, however, I realize that her fidgeting may have been related to the language (and, possibly, culture) barrier. The tutor, white, was dominant in the situation, whereas the writer, hispanic, was not.
They spent time going through sections of the paper, identifying where parts got confusing, which came down to word choice most often. The tutor read a sentence or two aloud and addresses an issue. The writier then begins to explain the story. (I should note that the essay was about personal identity, therefore, the writer fully undertood the stories told in the essay.) As she explained the story, the tutor asked questions that he then used to clarify and summarize the sentences already written.
As the session began to wind down, the writer asked is she will always have this "problem" and belittles herself as a writer. The tutor assures her that what she has spoken [about the assignment] made sense, and that a few extra words can bring two different ideas together the way that she has been trying to do.