Answer:
Install the most recent version of iTunes onto your computer if you do not already have it.
Open iTunes and click on "iTunes Store" in the panel on the left side of the window.
Sign in to your iTunes Store account by clicking on "Sign In" in the upper right corner. If you do not have an account yet, you will be prompted to create one later.
Click on "Redeem" on the right side of the window.
Scratch off the coating on the back of your iTunes card then enter the 16-digit code in the box under "Redeem Code" and click "Redeem."
Then you can Download.
Note these instructions are on the back of the card too.