I'm the co-founder a three year old critique group. We've had a 100% changeover once, but have had mostly the same people for the last two years. Most people start a critique group because they want their work critiqued, but if you're the leader, there are also some responsibilities. If someone starts getting argumentative during the meeting, it's your job to nudge them back in the right direction. If someone is in danger of running overtime, it's your job to get them back on track. If someone is just plain bad for the group, it's your job to encourage them to leave. It's also your job to set the rules for the group, and to enforce them.
For my group:
We are genre specific (thriller/suspense/mystery). This was a decision we made up front mainly because I have seen many people who really don't understand what a thriller is.
We critique two writers each meeting and meet once a month. They submit 50 pages about two weeks in advance. Fifty pages was decided on because it gives everyone an idea of where the story is going or if there are any problems. It's about 45 minutes or so for each critique. It doesn't seem like a lot, and in fact, both groups wanted to do more. But we've discovered that we really can't do more than two at one meeting (there are seven to ten members). And, we also know from experience that there's a point where everyone actually runs out of material.
We also require that the writers have at least 100 page completed before submitting anything for critique. We added this rule after two writers, both with three chapters done, gave up their projects after receiving critiques. Some writers want critiques to find out if their idea is any good, and the first three chapters are probably the worst thing to do this on.
Also, no arguing with the critiques, no defensiveness, no explanations. The writer isn't going to be standing over the agent's shoulder to explain confusing points; the story has to stand up for itself.
No booze. Though we do have lots of chocolate.
Critiques are done verbally in front of everyone (so noted because we ran across one group where they wrote the comments down and passed it to the writer; no one else heard the critiques).
The writer does NOT read their story aloud. Some groups do this, and we had a member who noted that she got very different comments from us than her read aloud group. She realized she had actually been adding extra nuances when she read it aloud, using her voice that changed how the people hearing it interpreted it.
Oh, and we do allow readers to join. We have two of them in the group now. The only real requirement is that the people can do critiques and should at least be familiar with the genre we're writing in.
And our general goal when we come there is to have fun.