Brotherhoods in game are created to unite players.
First of all you should build House of Brotherhood:
After that you will be able to join a Brotherhood. To find one, click the House of Brotherhood and select 'Brotherhoods' in the menu:
Otherwise you can click at the Brotherhood icon at the right bottom of the screen or press C on the keyboard:
A list of existing Brotherhoods will open. You can search for a certain Brotherhood and apply for membership:
Furthermore, you can create your own Brotherhood - open the 'Create' tab:
If you want your friends to join your Brotherhood, they should find it in the list and apply for membership.