The person who started a group can make it open or invitation-only.
You can see what open groups are available on a given course today. Just tap Start a New Round, select the course and select Group Rounds. Tap JOIN when you find a group you'd like to join.
You will need an invite to join an invitation-only group. Just ask the group organizer to send you an invite from round settings / group rounds. An invite can be sent via email, text message, Facebook, or by any other sharing method available on the phone. Once you receive an invitation, click the invitation link on your Android phone. Follow the prompts to join the group.
Note: Be sure you have Golf Pad version 13.0 or higher for Android and 10.0 for iPhone to access group rounds.