Although behaviorism is my least favorite approach to learning, anti-behaviorist Alfie Kohn reminded me one time it has a place is when you're not looking for long-term change. In other words, if you offer a healthy snack or an inexpensive desktop trinket to people who speak up, you won't help them participate in the next class (in fact, without a token they may actually contribute less), but it will encourage them now.
Some people prefer talking with only one or two others. Split the group into pairs or triads for a short time with a topic to dialog. When team time ends have everyone report on something new they learned or have them just savor their interaction and move on. Once people can talk with another person they might be willing to talk in the larger group too. If not, continue to use small group conversation throughout your time.
Various cultures (both organizational and regional) look down on speaking up. If you don't have an ongoing relationship with the group, ask whoever brought you in if there are politics or traditions in the room you should know about. Perhaps the discomfort people feel with someone else in the room overwhelms any urge to participate. This can happen when the group represents various authority or influence levels. Those with seniority may feel awkward alongside junior staff, and the frontline folks may be wary speaking with, or in front of, their chiefs.
Do you expect people to rev up before the coffee kicks in, or after a meal? Don't. Groups seem most chatty late morning, late afternoon and later in the evening. If you're facilitating a session which runs half-day or full-day, organize your topics and agenda so that early on you establish a strong information base and then as the day wears on people can contribute with comments and clarifications. If questions and answers feel too work-like, get people talking with a game or an icebreaker that builds trust. Encourage people to move around, have side conversations, and get comfortable in the setting.
"Don't be shy, p-l-e-a-s-e say something. Come on. Anyone?" delivered with passion calls attention to the situation and encourages people to overcome trepidation out of interest to not let you down. Repeating, "Don't be shy" will likely get you at least a few comebacks. If even that doesn't get the conversation rolling ask for small movement. "Nod your head to let me know you're with me," as you demonstrate by bobbing your head. The group will likely follow suit although probably a bit self-consciously. Encouraging, pushing, and cajoling may need to be continued for a while.
After using one or many of these techniques (sometimes in succession) the group usually yields, then chimes in. I recall a few times, including that with the librarians, when the pendulum swung completely and by the end of our time the group buzzed. At first the almost chaotic atmosphere felt uncomfortable too, but it served as dramatic contrast to the listlessness or defiance we began with.
And when nothing works? Remind everyone you're there as a facilitator of the knowledge in the room, not a lecturer or the sage on the stage, and you'll sit in silence until someone else contributes. Imagine the peace and quite which might ensue.