Good thread!
First time I accessed the net was at university in the late 90s. Initially on their PCs/Macs, and then I got my own PC. These machines (including my own) didn't have dial-up, but a much faster connection. It pre-dated broadband and download speeds were often around 320kb/s (roughly equivalent to 3mbit). Napster was big business back then and downloading an MP3 took just seconds. For comparison of internet speeds, home broadband didn't reach 3mbit until the mid-2000s.
Then I went back home for the summer holidays. The only option there was 56k dial-up which was a fraction of the speed that I was used to, but sadly it was the norm. The dialling sound was the same as the sound that a fax machine made.
Web pages (HTML) looked like Word documents, and you could edit/save HTML pages in Word too. There wasn't a dominant search engine back then like Google is now. There were lots of them like Lycos, Excite, Infoseek, Yahoo, Dogpile, Ask Jeeves, Altavista and Hotbot. The instant messengers were AIM, ICQ, IRC and Yahoo IM. I think MSN was just about there too but that might have been early 00s, not late 90s.
The scourge of the internet back then was pop-up ads and personal web pages such as Geocities, Fortune City and Angelfire. Internet providers issued you with you own webspace, so I made my own page instead of using ad-ridden Geocities etc.
Internet browsers were Netscape and Internet Explorer.
My email address was my university-issued one. The program we used for that was called Simeon.