I work for an ISP in the UK and we actually still have some of the old dial up internet kit running in our exchange, 99% of customers are now on xDSL based services, however a few are still belligerent and don't want to move into the modern age, the equipment doesn't really cost anything to keep running so it's in effect free money for the business (other than power).
The technical side is basically a few Cisco AS5300 that terminate 2 to 4 E1's from the IMS based ISDN network, your effectively just dialling a number from your modem that is load balanced over these E1's. At the other side of the Cisco is your internet service, fairly simple and works well for what it is.
There can be other things in the mix like AAA (Radius) to authenticate the users, but as your charging for the call within the POTS network that's not always required, assuming that the internet and line provider as the same as in our case.