Personally, I don't have the game, but I would assume the option is available on the main menu. I did some research and it looks like you have to beat 4 missions in the single player mode before the option to play extinction is unlocked. Hope this helps!
How to Unlock Extinction Mode
1. Start the Campaign under Regular difficulty or higher. Extinction Mode will not unlock under Recruit.
2. Complete the first four (4) missions. Finish Ghost Stories, Brave New World, No Man’s Land, and Struck Down.
3. Finish the fourth mission and return to the main menu to see the new selection; Extinction Mode.
1. Start your Multiplayer Career.
2. Reach Level 5.
3. Return to the main menu to find the new selection; Extinction Mode.