Missions are how you will earn rewards and generate Corruption or Suppression.
You can access the Mission Log with (G).
You can then navigate through the different missions to see its details by using the (1), (2), (3), and (4) buttons.
You may want to cycle between missions with different requirements. The mission Restitution, for example, requires you to retrieve 20 Schematic Cryschips and deliver them to a Field Depository.
While in Cessation you must activate 5 Power Junctions and then install a Broadcast Node.
Once you've chosen the mission you wish to complete you can use (F) to accept the mission.
You will need to activate a tracker by pressing "H" to keep track of the mission progress in the top left corner of your screen.