One way to involve a child in an activity is to involve them from the start. This means that you set the ground rules upfront and let them know what is expected of them. For example, you might say that they need to participate by following instructions, being cooperative, and keeping quiet. Another way is to choose an activity that your child is interested in.
This can help get them out of their comfort zone and into new surroundings. If they are not interested in participating, try choosing an activity that they are.