This'll be short and sweet.
Never underestimate the power of praise. When a student answers a question in class, tell the student what they did right, instead of focusing on what they did wrong. Even if an answer is completely wrong, I will most likely thank them for trying. I might even tell them they did a great job, although the answer is not what I was looking for.
When a student is praised, the student will be more inclined to participate and less scared of rejection. Encourage your students to try. Of course, remind them to think about their answer before they raise their hand, but after sufficient thinking and waiting time, they should feel comfortable trying and possibly failing.
Take failing or losing out of the equation. You can either win or learn.