Yes, with the new account you have made you will recieve one months free xbox live with that, that's only if it's a new xbox console. Once you have made the account etc. You need to hit the xbox button (middle of tue controller) and slide as far left, and you'll see 'redeem code' click that an enter in your live code.
Personally if it's a new console I would make the 1 month trial account a tester online, just so you get used to xbox. Meaning if your KD on call of duty is low, it wouldn't matter because it's not your main account.
Thanks, hope this has helped.
Retro.