The commercial agreements determine a lot of the complexities of how you receipt and mange payments from customers. This video is a quick walk through of the basic accounts receivable payment (or receipt) processing flow. In AX the receipt journal is called a payment journal just because you are processing a payment from a customer.
This video has a walk through of the setup of invoices to process for payment.
This video was recorded in AX2012 R2 but the same concepts apply to any release of AX2012.