PaymentGroup is way by which you pay the order. PaymentGroup have properties like type (options are creditCard,giftCertificate,storeCredit) , paymentMethod, amount, paymentStatus .currencyCode, submittedDate ect.
There is no property like method. Also in OrderTools.property file you have defaultPaymentGroup=CreditCard.
Can you give more info. about which method do you want to know?
In design terms you can say that a PaymentGroup object is an abstraction for a payment method. In ATG, PaymentGroup is actually an interface to represent all the information related to a payment method that is going to be used for purchase. There are some default implementations for PaymentGroup provided OOB in ATG like CreditCard, GiftCertificate, StoreCredit and InvoiceRequest (for B2B). Now if your application requires support for a new payment method say like Cash-On-Delivery then you would need to create a corresponding PaymentGroup and extend the payment process to support the new payment method.
as you can see in the http://docs.oracle.com/cd/E35318_02/Platform.10-1-1/apidoc/index.html
the PaymentGroup is an Interface , and implemenation classes are also metioned .
you might want to see the documentation for clear explaination http://docs.oracle.com/cd/E35318_02/Platform.10-1-1/ATGCommProgGuide/html/s1508processingpaymentoforders01.html