You can interact with other Lords and Ladies from the Map interface by opening the Map, finding another Lord or Lady's Castle, and then choosing an action from the Action menu. In order to attack a Castle, tap on the Map button in the lower left hand corner of the screen and then select the Castle you would like to attack. Now, assemble the attacking army and send it to the Castle you have chosen. If your Raid is successful, you will seize a certain number of Resources.
Remember to spy on your enemy's Castle first, before launching an attack!