Had my first email address as a student at University, in my final year as an undergraduate, so would've been mid-1993...and can honestly say, I thought it was just a novelty (especially as I didn't know anyone else with one!)
In my first year as a post-grad, I started using the Internet, probably early 1994, and remember a mate of mine showing me how it worked. At the time there were no search engines, so you found web sites on massive index sites hosted by places like CERN. I also wrote and published my own web pages in basic html, and at one time had one of the most widely visited and linked-to sites relating to Real Ale in the UK, getting a few hundred visitors a day from all over the world!! I was even offered a job to write and design web pages, but wasn't remotely interested (if only...!) and wanted to finish my course.
And I remember the wonders of MCIVTA, a City newsletter/fanzine that used to be circulated a couple of times a week, and then I realised the power of the web!