I have the game, and I'm enjoying it
I've only done one Shadow War so far, as I've had limited time with it and am still learning the ropes. It was a little confusing, and I didn't have decent weapons on me, but it certainly showed promise.
You can access it through the matchmaking section in the main menu (push start-hold left trigger-select matchmaking on wheel), but the quickest way is to press the d-pad (left or right, I can't remember, but it'll be obvious with the on-screen info) then keep pressing right to select matchmaking-shadow wars-join (or words to that effect).
It will put you in a queue, so you can carry on with what you're doing and as soon as a match is available it will move you over (mine started instantly, you can cancel with the dpad commands as well).
Playing on 360, so don't know the PC commands but they'll be similar to the above.