Summarize:

Once it's up and running, press the iTunes Store button on the Navigation bar on the right hand side of the screen. If you do not have an iTunes account, you will have to create one. Download iTunes from their website if you need to. It's free and the folks at Apple make it pretty straightforward. Once you've got the program on your computer, create an account and sign in. Your email should pop up on the left hand side of the bar along with "Music," "Movies," and all your other choices.  If you have a remaining balance, that, too, will pop up next to your email. Watch for that to change once you've registered your gift card. If a different account is logged in, click on the email being displayed and select "Sign Out." It'll then prompt you to sign in with a different email. There are two ways to do this:  On the panel on the right side, "Redeem" can be found under Quick Links. It's next to "Account," "Purchased, and "Support." Click on your email on the toolbar. It'll then give you the options of "Account," "Redeem," "Wish List," and "Sign Out." You may have to scratch off the grey box on the back of your card to reveal your 16-digit number. Each code tells Apple how much your card or certificate is worth. Once entered in correctly, a box will pop up telling you how much your account has been credited. Check on the iTunes gift card what country of iTunes it can be used on; they are not interchangeable. So, if you are on the wrong country's version of the site, you'll need to go to the very bottom of the store's page and press My Store. You will then be able to pick the country of your choice. Buy any of the songs, videos, audiobooks, games, TV shows, or movies of your choosing. iTunes will require your password for any purchase and not let you go above your balance unless you have credit card information otherwise provided.
Open up iTunes. Verify that you're signed into the account you want to use. Click "Redeem" on the screen of the iTunes Store page. Enter your code. Start shopping.