1. Recognize Your Responsibilities. Your role as leader gets bigger and more challenging in direct proportion to the lack of extroverts in your group. Before introverts will get verbal, they need to 1) trust the leader; 2) trust each other; and 3) trust that they have the correct answer to any given question. While extroverts are not ruffled when their verbalization misses the mark by a mile, introverts insist on accuracy before they are willing to make a peep. They will not speak until they are sure they are correct and safe, and even then, they prefer a good-sized margin for error. Build their trust.
2. Plan Ahead. The less you feel your group will participate, the more prepared you will need to be: Come with lots of questions, follow-up questions, examples of answers, and funny stories with which to carry the silences. When asking questions of a quiet group, each should have an "obviously right" answer, and should be followed with an open-ended 'personal" question like why, or what would you have done in that situation, or what other options did this situation provide, etc. Be prepared.
3. Provide Advance Notice About Their Role. State clearly and early on during the meeting that you look forward to hearing from each participant at some point. Further clarify that you will be calling on people to respond to the different questions. Be aware that many introverts are retro-processors: Their reluctance to answer stems from their need to think through things before being able to respond with confidence.
4. Provide a Silent "Buffer" Zone. Introverts have at least as many great ideas as extroverts; it's just that they are far less willing to share them. In most meetings, the extroverts in attendance respond so quickly and frequently that the input of the introverts gets lost in the mix. So, if your extroverts are absent, take the opportunity to dig for hidden treasure! Give each person a piece of paper and a writing utensil. Provide time after each question for them to jot down their ideas before you open up the item for general discussion.
5. Build Trust. If your group is very shy, start the discussion time by counting them off into groups of two. Ask the first question and provide the follow-up question. Then, A) Give each individual time to write down a few ideas; B) Verbally tell them to share their answers with their partner; C) Randomly request that one person share their partner's answer; and D) Require them to quickly find a new partner before you start the process again. After a few rounds, have them move into teams with three to five partners and then continue. Finally, bring the larger group together for a few questions.
6. Tackle the Talkers. It seems like there is always at least one extrovert who is bent on the avoidance of silence at any cost. This person may resort to ridiculous lengths to maintain a steady stream of chatter. If you have noticed this in advance, come prepared with breath mints or some other individually wrapped candies. Whenever someone makes a notable contribution, toss them a candy. If someone is getting "all the candy," make a verbal joke about it and, if it persists, request that they let others have a chance at it.
By embracing the unique needs of your introverts, you will turn an apprehensive assembly into a gracious group of team players. By the end of your meeting there will be free-flowing conversations that will most likely spill into the hallways afterward.
Upon the return of your chatty constituents, build on the confidence you developed during their absence. Retain the safety nets described above, at least until there is a high level of trust between all of the leaders and participants.
In addition, continue using the format of a safe question with a follow-up discussion question. This will not only keep your introverts involved, but will also teach your extroverts the value of answering correctly the first time. In addition, they may be shocked at the untapped wealth of wisdom sitting right beside them, whenever they choose to be quiet long enough to listen!