Instructions
Locate the mini-map on the bottom right side of the screen. The mini-map houses icons for important people, a layout of the environment and objective icons. Objective icons are the black, flashing icons that represent missions that can be accessed immediately.
Use the directional pad to move Altair to the objective icon. Most objective icons represent a person that must be talked to to activate the mission.
Talk to the person with the objective icon over their head by pressing the "X" button. In some cases, simply moving within the vicinity of the icon will trigger the mission.