To access co-op simply press the Up button on your controller to access your mobile phone, then go down to the 'Online Contracts' section about halfway down. Press X to access it and then it will bring you to the online contracts menu. Select the mode on the top right corner of the screen called 'Online Street Sweep'. Or you can press the touchpad and press R1 to get to the Online contracts menu. You will then be able to find a partner and play some street sweep missions.
You can play any of the three types of Street Sweep contracts, Militia, Chicago South Club or Fixer.
Some tips while playing co-op:
You can only fail the mission if both players die. If one player goes down he will get 10 seconds before he can respawn. As long as the other player does not die the player will be respawned and can continue as normal.
Flank your enemies. If your partner has got the attention of your enemies, sneak round the back of the camp and take out the enemies while they unsuspect it.