Q: How do I change payment options

If you aren't getting the 'none' option then do you owe iTunes anything or have any pre-orders/subscriptions due : http://support.apple.com/kb/TS5366 ?

Or is it an account that you're trying to use in the store for the first time - unless the instructions on this page are followed when creating an account : http://support.apple.com/kb/HT2534

then credit card details will need to be entered before the account can be used to download any item from the store.

If you are being prompted to review the account then you could see if this post by mountaingoatgirl lets you do so without needing to enter credit card details : https://discussions.apple.com/message/24303054#24303054