Paypal is our credit card processor online. We use them for the security of online payments. It's fast and easy and allows you to also choose to pay through your bank account (provided you have a Paypal account with that option set up).
You may use this service whether you have an account with Paypal or not but keep in mind that as a security measure, Paypal only allows you to charge a lifetime (the credit card and not yours) amount of $750. This prevents major fraud charges from happening. If you pay online without an account and get declined, it's very possible you have reached this maximum.