They are using a small protocol (XML or plain ISO8583) over a somewhat fast connection (X.25, GPRS, 3G or the store's internet - ADSL, etc). Connections are always kept alive for a certain amount of time.
The bank side of processing is very simple and shouldn't take long. Keep in mind that the data used to authorize a transaction is minimal. After the authorization is given, the bank will process the actual payment, which is a two-step job with the first step being executed minutes after the purchase and the second one usually at night.
I wouldn't recommend you digging too much into banking standards without a specific purpose. There are just so many and almost no one strictly follows them. This is a good start: http://www.aba.com/Pages/default.aspx and https://www.pcisecuritystandards.org/