Appreciations are one of my go-to tools when assisting teams in building trust. They’re also a go-to tool for more mature teams, as we can never receive enough appreciations.
Give each person space to offer an appreciation. Round-robin style tends to work well at first, especially if you have a number of people more on the tentative side. Popcorn style, where people speak out in no particular order, tends to work better as the team builds up trust. However you organize things, be clear that participation is optional. Requiring people to give appreciations is a sure-fire way to make those appreciations meaningless.
Offer your appreciation using the form <Person>, I appreciate you for <reason>. Describe a specific action the person took and the specific effect it had on you. The more concrete and detailed you are the more meaningful your appreciation tends to be.
While you may be tempted to appreciate each person on your team and every person you work with, resist! The more appreciations you hand out at a time the less powerful each one is. Similarly, do not try to ensure that every person receives an appreciation each time. The more singular an experience receiving an appreciation is, the more that experience will be valued and (pun not really intended) appreciated.