I was on it pretty early, like 92, with Prodigy at first and then AOL/CompuServe/etc. later. I remember our first modem was a 2400 baud which I upgraded to a 14.4k later and that was a pretty big deal. When 56k came out it was a huge deal, I remember thinking how fast it was.
But yeah you just connected via your phone line to your Internet Service Provider (ISP) and then you were good to go. We installed a second phone line cause we used it so much. Your only extra charge was to your ISP, you didn't have to pay anything extra to your phone company really cause it was just a local call connecting to your ISP.
Kids these days have no idea of the struggle back then man