IME, in order to help a group solve a new problem a facilitator needs to do two things. The first is to create a meaningful meeting purpose and agenda that can achieve the goal of the discussion within the allotted timeframe. A meeting purpose and agenda sets the objectives of the discussion and helps the participants understand their role in the meeting. Most meetings fail here.
The second is to apply facilitative listening skills while the group is in discussion. When members are working to towards developing a sustainable solution, facilitative listening skills support participants in each phase of the dynamics of group decision-making – divergence, integration and convergence. This cheat sheet, taken from the book Facilitator’s Guide to Participatory Decision-Making by Sam Kaner et al., provides a list of thirteen listening techniques that allow facilitator to offer on-the-spot care and support as group struggle to work through the Groan Zone.