Follow these steps to redeem your Xbox Live Gift Card:

  1. Visit redeem.microsoft.com and sign in
  2. Enter the Xbox Live Gift Card which you can find under My Withdrawals by clicking on "Show Code"
  3. Follow the prompts, don’t worry about hyphens, the system takes care of those for you
  4. The balance has now been added to your Xbox Live account


Note: You can find the official instructions here.