I'll start with a verbal description for now - and will make a note to add screenshots later on once we have them (we are preparing them as we work on updating the help pages).
At the end of each transaction (membership application, event registration etc.), user is presented with transaction details (e.g. membership form with all fields) and asked to confirm the transaction. Once 'confirm' button is pressed, system generates an invoice for this transaction and user is transferred to 'Invoices and payments screen. If this the only/first transaction, the screen will have one line with the invoice in question - and payment instructions.
(Otherwise, old invoices and payments will be listed below as well. Unpaid Invoices are presented at the top and more prominently formatted)
If online payment is setup, user would click on 'pay online' and proceed to pay (pretty much as before). Otherwise he/she would just read payment instructions and send the payment somehow outside of Wild Apricot.
Alternatively, user can leave this screen and start another transaction, e.g. event registration. In this case, upon confirming that transaction, user would end up on Invoices and payments screen with two lines - two open invoices. It is then possible to select one or both and pay online.
Dmitry Buterin, Chief Apricot