You can leave a group by clicking on the "Click to leave this group" link at the bottom of the right sidebar on your participate page, and then confirming your decision.
After you leave the group you will no longer be able to access your participate page or get notices about group discussion. You will have to re-apply if you want to join again, and be re-approved by group administrators. All actions you created that are sponsored by the group will remain as they are -- you will still have access to them, but so will group administrators.