The basic process of accepting a payment is fairly straight forward in AX. The complexities will come with the types of vendors, payment methods, processing periods, cash discount approaches etc. This video gives a basic overview of processing a check payment to settled a number of vendor invoices.
This was recorded on AX2012 R2 but the same concepts apply to any version of AX2012.
This video covers the entry of the invoices for setup of the payment.