At some point in your career you may be asked to be the Session Chair at a conference. If asked, you should accept, if possible. It is an easy job, and it is a service to the research community.
Usually by the time you are asked to be a Session Chair you will have attended several conferences and will already be familiar with some of what a Session Chair does. However, like many jobs, there is more to being a good Session Chair than meets the eye. Below is a brief, semi-chronological description of a Session Chair's duties, and some advice on how to accomplish them.
Show up during the break before the session, and help the authors get their laptops or other A/V set up. Most authors are competent, so this is pretty easy, but every once in awhile someone needs help. If an author is not showing up, go track him/her down so they get the A/V done before the session starts.
Find out how to pronounce author names, and practice it a couple of times so that you don't mangle names when you introduce speakers. Easy to do, and very important.
Find, or make, signs indicating how much time the speaker has left. I like "5", "2", and "Stop"; your preferences may vary.
Claim your seat (put something on it now). Pick a spot as directly in the speaker's line of sight as possible. This is a challenge, because speakers don't always look where you expect, but try. Don't assume they will look over at you during their talk, even if they promise to. They'll be thinking about their talk, not about you.
Tell the speakers where you will be sitting, and when you will flash your signs at them, so they'll know what to expect.
2-3 minutes before the session starts someone should warn people that the session is starting, either by flashing lights or wandering around saying "We're getting started now". It might be you, or not.
Start the session on time. You may want to wait for the audience to trickle in, but don't. If you start late, you end late. People will wander in when they hear you getting started.
When you start the session, introduce the session title, optionally introduce yourself as Session Chair, maybe say a few words about what the session is about (i.e., stall a moment while people trickle in). Remember, you're not the star of the session, so keep this brief.
Introduce the speakers (remember how to say their names), help them get the mike attached, then go sit down.
Watch the time. A minute before a milestone, start trying to catch the speaker's eye, i.e., start at 6 minutes for the 5 minute sign. Some speakers are easy to catch, some are impossible. Do the best you can, don't let it ruin the talk for you. If someone runs into their Q/A time, but is obviously winding up, let them. If someone is almost through their Q/A time, you'll have no choice but to be more forceful (i.e., say "1 minute" loud enough for them to hear you, or stand up). It's rare that you'd need to go that far, but it happens.
If you can, it's nice for the Session Chair to have a question in reserve for each speaker, in case the audience has none. It shows that you're on the ball, and authors appreciate it. You can either do this on the fly, or read the paper ahead of time.
Some Session Chairs manage the Q/A process, e.g., by picking among the people with raised hands. Some allow the authors to pick for themselves. Your choice.
Ideally each Q/A exchange lasts 1-3 minutes, to allow time for several questions. If it looks like a member of the audience is dominating the Q/A time, e.g., by making statements (instead of asking a question), or asking multiple followup questions, you should help the author by suggesting that the discussion be taken offline. This doesn't happen often, but it does happen.
End the Q/A on time, otherwise the session will run late. Use judgement about this; a minute or two overtime for someone asking a scintillating question is fine, but your job is to keep things on schedule, so exceptions should be rare.
Thank the speaker, lead the applause, and move on.
I hope that I haven't made the job sound difficult. Usually it is easy, and usually it indicates a certain level of achievement / status, so it's a good thing to do.