Internet began its Cambrian explosion in 1993, I would say, with the release of the Mosaic web browser. Before that the internet had existed for a long time, but it was mostly e-mail, telnet, ftp and simple services. The World Wide Web was the hype of 1993, and it coincided with dial-up services for the general public, and I think that by 1995 most had realised that the World Wide Web had come to stay and had become synonymous with internet.
My life has been well timed with computer technology, I think. I grew up with computer programming on Commodore computers in the 80'ies (Vic-20, C64/128, Amiga). Not before had computing been so accessible. And when it was entirely clear around 1992 that the Commodore Amiga was going nowhere, I began at the university, got on the internet and learned about Linux which was maturing, became capable of running X Window and compatible with everything at the university. I saved up some money and bought my first PC in 1993, with 16 MB of RAM and a 17" monitor (usually PC's were sold with 4 or 8 MB and 15" monitors at that time), installed Linux, and I didn't really needed to leave my dorm any more apart from going to lectures.
In 1992 I began playing MUME, a text-based online Middle Earth online game, and got slightly addicted for a few years. Interestingly, the game still exists in its original format. I just logged in with my 25 year old player, and there were 50 players online.