To create a new faction, go to the 'character' menu in the TESCS and select the 'Faction' option, then enter the ID, name etc of your new faction in the relevant boxes. Setting rank requirements can get a bit repetitive, though.
You can also set modifiers which determine how well or ill-disposed members of your new faction are towards members of other factions.
Is the player going to be a member of the faction? In order to account for the faction's loyalty to the player, you could set the player's faction rank to the highest possible upon joining, and also set the player's faction reputation.
Alternatively you could create a second new faction which has the player as its only member, and set the disposition of the NPC faction towards the player faction to ensure extreme goodwill.
Hope this helps.