You can press that full stop button underneath the > sign and the group window will pop up. In the search tab you can type in the name of a group, click it again and options will appear. Choose send request or something like that and the leader of the group will either accept you as a member or reject you.
To create a group you must not be in a group to start off with. In the middle tab you type in the name of your desired group name and then click the Create button. In the chat box it will tell you if the group name is taken or its been created successfully.
To send invites you must be the group leader (The person who created the group) you can double click someones character and choose the option Send Group Invite. This option will not show up if their character is in another group.
