The easiest way is to obtain an Apple iTunes gift card and then use that to open the iTunes account. If you have an alternate form of payment to open the account - like the gift card, you won't need a credit card. You can purchase a gift card at many stores including Target, Safeway, Best Buy, etc.
Ok people have been having trouble with this for a LONG time,what you want to do is go to an app and click install and when it asks you to make a new apple ID tap new apple ID then fill out your information and when it says credit cards there will be an option saying (None) click on that and continue filling out the other information. Once you have verified it with your email,you have created your apple ID.