There are different kinds of group counseling, and some of those groups have steps in them that are specific to a group of people confronting a certain type of issue. That being said, quite frequently group therapy will start with check-in, where everyone in the circle gets to check in and say how they are doing. This is usually limited to a couple of minutes each, so that one member will not take over the group and decide now is the time to tell their entire life story. Also during check-in group members might be invited to bring up topics for the group to discuss on that day. (There are also some groups that have a curriculum that the facilitator wants to be the focus of the group.)
The majority of the time in the group is likely to be spent discussing the topics participants have brought up that they want to discuss. Sometimes group members don’t have topics to suggest and the facilitator will initiate discussion on some topics. The facilitator works to make sure that everyone has an opportunity to participate if they want to, that everyone is heard, and that everyone is safe. If a group member starts saying something negative about another group member the facilitator will reassert the group rules the participants have developed and agreed upon about how everyone is going to treat each other in group. They will advise someone kindly if they are off topic. They may suggest that the off topic comments can be saved for discussion later.