Well not directly using it myself, but I do have a very clear, specific memory of first hearing about it. The end of my junior year of high school in early summer 1993, one of the seniors I was friends with was going to college in Ithica NY in the fall and he was telling us about this new thing called "electronic mail" that we'd be able to write to him thru the computer and he'd be able to see it right away.
I remember buying my first computer (that had internet access), sometime in the winter of 1995/96, I went into Delaware as the PA/DE border was very close to my work and I went to a Best Buy there specifically to avoid the added cost of state income tax. It was a Packard Bell, with a whopping 1gb of hard drive storage (actually less than that after the pre-installed software). But I don't have any specific memories of first going online.
edit: oh though I do remember a bit later on, my older brother had already had a computer for awhile, and at the end of one visit to his & his (now wife)'s apartment, he slipped me a piece of paper and told me to go to "naughtylinx.com"