To join Open Factions, tap on the "Faction" icon located in the lower-left corner of the screen. When you are not a member of a Faction, you can go to the Join tab in the Faction menu and it will show you a list of Open Factions. You can immediately join a Faction whose status is Open. For Restricted Factions, this type of Faction requires you to fill out an application and send it to the Faction General. From the "Apply" tab, you can send an application to Restricted Factions. This will send the application to the Restricted Faction's General to approve your join request.