Note: An unredeemed iTunes gift card or code is needed for this guide.
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I learned this on About.com and made a Snapguide for it.
Go to the "App Store" icon.
Go to the "Featured" icon in the bottom bar.
Go to the "Sign In" tab.
Go to the "Create Apple I.D." tab.
Choose your country in the "Store" tab.
Press the "Agree" tab.
Add in your email information.
Add in your security information.
Add in your optional email information.
Add in your DOB information.
Choose whether to subscribe to Apple emails.
Scroll past the credit card information boxes.
Now, enter the unredeemed iTunes gift card or code.
Add in your billing address information.
Add in your information. I just use a 555-5555 number.
You have now created an Apple I.D. without a credit card. This is particularly useful for kids with an iOS device, or a person who does not like giving out credit card information.