To join a group, click on the Groups tab at the top navigation bar. If you have not been assigned to a group, you will see the Join button next to the available groups. Click the button to join the group you prefer.
If you were already assigned to a group or joined one by yourself, you will see the green checkmark icon next to Joined. That means that you are part of that group from now on. If you want to move to a different group, click on Move to this group at the far right of the group you want to move to.
Click on Show Members to check the members of your group and the other groups. You can also click on the envelope icon to message all your group members at once.