I am doing my PhD and presenting a paper at a conference, which I have already done a few times. However, I just saw an email from the organising committee asking if I am willing to chair one or more sessions. How should I decide whether to accept this offer? What are the reasons to accept, and what are the reasons to decline? Is it a very common thing to do for a graduate student, who does not even have a Ph.D, to be invited to chair a session? While I feel honoured, I am also somewhat overwhelmed and not sure if I should accept it.
Yes, you should.
Whether this is common depends very much on the conference. The last time I was at a conference, I was invited out of the blue by someone I didn't know to chair a session, in a very short and very informal e-mail as if it was coming from a long time friend in a hurry. This was less than a year after I obtained my PhD. A PhD student in our research group did the same.
All it means, really, is that you sit on a chair in front of the room, make sure the presentations are on the presentation computer, announce the speakers, etc. You will get detailed instructions. Unless you mess up (and why would you?), you really have nothing to lose.
The typical duties of a session chair are:
These duties aren't too hard, and it's not too unusual for senior graduate students, postdocs or young faculty to be asked to chair. It's a nice little low-grade visibility and networking experience, and can be a first (small) step towards becoming involved with other aspects of conference organizing.
The only reason that I might recommend against accepting is if the session is early in the conference and you haven't been to conferences and seen how sessions are typically run before. This is something where I would recommend making sure you've watched others before you do it yourself---though you will see many bad examples as well as good.