Another technique to draw out group members is the use of a 'round' in which every group member is sequentially asked to volunteer information without commenting on the previous individual's words. This ensures that every member of the group has to participate but makes the experience far less threatening since everyone is speaking and the reluctant member can be less worried about negative feedback, since participation takes place in a non-judgmental context. Not all exercises and techniques to draw out group members need to be so formalized, of course. Simply using friendly eye contact can make group members feel more welcomed and eager to participate. Activities that can be useful for all members can have the added benefit of drawing out group members. For example, having group members interview one another on the first day and 'present' their interview subject when the group reconvenes is one way to encourage all participants...

Giving group members 'homework' or writing assignments and allowing them to read selections aloud at the beginning of the next session can relieve some of the challenges people experience speaking spontaneously.
Regardless, many of the issues which arise with overly dominant or quiet members highlight the importance of having an effective formative stage of group development: the rules and relationships must be established early on which create a comfort zone for all group members. Of course, these rules may shift and change as the group evolves but ideally the group should have a positive atmosphere from the very first meeting onward to set the tone of all subsequent group sessions.

Reference

Jacobs, E. (2012). Group counseling: Strategies and skills. Thomson Brooks/Cole.