1) Redeem your Season Pass code through the Xbox Guide: http://support.xbox.com/en-US/billing-and-subscriptions/prepaid-codes/redeem-prepaid-codes
2) Depending on the code, this will either add 2400 Microsoft Points to your account or automatically redeem the Season Pass.
3) In the main menu of Borderlands 2, Select “Downloadable Content”
If you your code automatically unlocked the Season Pass, skip to step 4; otherwise continue with the next step (A).
A) Select Purchase Season Pass.
4) Select “Captain Scarlett and Her Pirate’s Booty” (Free) to begin the download.
Do NOT select the version that costs 800 Microsoft Points.