To unlock co-op multiplayer, you'll need to complete the tutorial mission and three missions of the campaign. As part of the strategy map tutorial, your University will then be attacked, and you'll see a message on screen saying co-op has been unlocked.
If you return to the Menu Menu now, the JOIN option will appear where you can join another online game. From the PLAY menu, where you choose your save slot, you'll now be able to host an online game when you continue, or start a new campaign in either single player or co-op.
(Any new campaigns started from this point are playable in co-op from the beginning. Note that new campaigns will start from a random location and with a random weapon selection).

To play split screen co-op, you can either choose Split Screen from this menu or join during a single player game at any point from the pause menu, or by connecting a 2nd controller and pressing the A button on it.*
* (Playing split screen with one PlayStation and one Xbox controller connected is not possible).