Speak with the student and ask if he or she has spoken to the instructor about the issue. Surprisingly students sometimes skip this obvious step and many concerns can be addressed in that way. Of course, sometimes the student does not feel comfortable speaking with the instructor and if that is the case then I would speak with the student. Make contemporaneous notes.

Hear what the student has to say. Generally I find that it is wise not to offer any judgment on what you think is going on (in fact I never did so). Listen to the student and make sure that you are clear about the nature of the complaint. At that point I would say that I would speak to the instructor, assuring the student that his or her name would not come up.. I typically would also make clear to the student that each instructor is the final judge of grades and appropriate requirements for the course. I suppose this could vary somewhat depending upon department but in my department, within the bounds of following the course outline, this was true.

I would then speak to the instructor. Frequently the result would be that it was clear that the student had misunderstood a requirement or what the point of a particular assignment was. The instructor could then clear this up and the problem was solved.. If this did not resolve the problem I would propose a meeting with the instructor and the student where we would try and work it out.

For me, the key things to keep in mind in these circumstances are that all parties need to be listened to, that the student wants to feel as though they have been heard. Students will accept outcomes that are not what they most desired as long as they feel that they have been fairly treated. The criteria for making decisions need to be made clear and that they have been applied fairly needs to be seen.

One further comment -- Chairs of multidisciplinary departments need to be aware that different disciplines operate in different ways. This may be relevant in considering student complaints. It is rarely the case that it is appropriate for the chair to determine what it is that the instructor ought to be doing in the classroom. I think it is important to keep in mind that the goal is to resolve the dispute not make a judgment about what is the right course of action to resolve the dispute. That being said, it may be the case that once a problem has arisen the instructor will request that the chair suggest a resolution. In such a case having some suggestions for how to resolve disputes on hand might be good.