> Does this mean that, on either side of the connection (the home network and the ISP), there is a modem involved? So the connection goes from a modem at the home network, through the telephone line, and connects to a modem at the ISP?
Yes, exactly that for dialup modems. This is actually no longer used by ISPs, but ISPs used to have rack-mounted banks of modems that were connected to the phone system. As customers dialed in, the phone system at the ISP would roll over to the next available modem, and the customer modem would connect with the ISP modem.
For xDSL, the ISPs now have neighborhood DSLAMs (Digital Subscriber Line Access Multiplexer) to which the customer "modems" connect. These will terminate the customer lines and multiplex the data on to the ISP central office over one or more other lines. This saves the ISP from having to run a line for every customer from the CO to the customer.