At no point in the signup process or creation of your Yola account are you required to submit credit card details if you do not wish to make a purchase. Site building and hosting with Yola is completely free of charge.
For more information on what you can purchase from Yola, take a look at this link.
If you wish to purchase some of these features, only then would you need to use either your credit card or PayPal account for the payment.
All of these paid features are entirely optional. You can still publish your site to a free Yola subdomain and use a free style on your site if you prefer. Your website can either be completely free or you can incorporate some of the paid features, depending on your needs.