You must liberate each area of Rome by killing the following Borgia Captains and igniting the Borgia Tower of each area that is marked on your map. After liberating an area you can recruit Assassins for the Brotherhood and renovate shops and other things in that area. The captains are located in the corresponding districts:

CAPTAIN - DISTRICT
Iacopo de Grassi - Centro District
Pietro da Siena - Centro District
Domencio da Padova - Centro District
Belardino da Verona - Centro District
Valentino da Siena - Centro District
Prospero da Siena - Antico District
Tommaso di Viterbo - Antico District
Ippolito di Foligno - Antico District
Franceso da Velletri - Campagna District
Antonio da Fiorentio - Campagna District
Battista Borgia - Campagna District
Ferdinando di Napoli - Campagna District