To offer your costumer the payment method "credit card" you either use PayMill or Stripe. Both ways you have to have or be willing to open up an account there. Here is how it works:
Credit card payment via PayMill
Hit "payment methods" > "credit card payment (PayMill)"
Choose the countries in which this payment method should be allowed
Enter a price if your costumer has to pay an extra fee for using this payment method (not recommended)
Fill in your PayMill public and private key
Save and you're done :-)
Credit card payment via Stripe
Hit "payment methods" > "credit card payment (Stripe)"
By hitting "connect now" you are automatically transfered to our interface with Stripe
Enter all necessary information and hit "Zugriff auf dieses Konto aktivieren" and the new payment method is activated
+a wide range of available credit cards are accepted worldwide (Visa, Master, American Express...)
+immediately pay in a convenient way
Other payment methods under http://helpcenter.branchbob.com/branchbob-helpcenter-english/activating-payment-methods