Am helping my BFF and fellow Tim Riggins lover Shelly with a super fun TILT group at Lewis & Clark Middle School today, and we ran into this problem. You SHOULD be able to create a new AppleID without using a credit card by following these steps.
However, if you run into trouble like we did, where the "None" option isn't available under "Billing Information", (AHHH!) check out this great blog post to see how to work around it. Essentially, you will go into the App Store and add a free app, then create a new AppleID when you're prompted to do so. For some reason, this prompts the "None" option to appear under payment. Teachers can select and continue creating their AppleID without entering credit card info.