When running groups, you will often have the unexpected to deal with.
Here are some things I find helpful.
Start with positive things “What is working well?”
Explain again the background to the task in hand and your involvement so far. People are often anxious about new situations.
Keep an eye on the time and make sure everyone has a chance to contribute before time is up. If possible, give people equal time.
Put your own ideas in the pot at some stage, but do not defend them. This relaxes people.
If in doubt, listen.
When you listen, look at the person speaking.
Summarise at intervals what the group and individuals are saying.
Try to get people to share their views and opinions rather than debate specific issues.
Do not argue even if you violently disagree with a point of view.
You can discuss serious topics lightly. A little humour helps.
When people find participating difficult and show it, it is probably not your fault. The reason is often in the past, a simple acknowledgement and warm attention will often help “You seem to finding today difficult, can I help?” Then just listen.
Your feelings are often a guide to what is going on in the group. It is useful to ask how people are feeling if you suddenly feel uncomfortable. It is probably a simple thing that you can easily fix.
Remember that however it appears, people, including you, are always doing the best they can. Blaming is not helpful.