Go to your Castellan and tell him you wish to send out recruiters.These new units will be the units of your faction's culture, so if your faction is House Targaryen, the town will now recruit Targaryen units. Click the 'Recruit troops' option and provide the fief with money to purchase new units with.
To recruit this unit, the player has two options: Currently, there are only 2 ways to obtain Targaryen units and both of these require the player to own a castle or town, as well as being either a vassal of House Targaryen or having their own faction with their culture set to House Targaryen. Because House Targaryen has no native lands, there are no villages where you can recruit their units. The Targaryen Man-at-Arms is the most basic unit of House Targaryen and will promote into the Veteran Targaryen Man-at-Arms.