Was somewhat informed of it on Gaia when I was 13, was in the Sonic (specifically Sonic Paradox) fandom and found FA art and fursuiting videos when I was 14, and decided to join FAF then FA when I was 15.
I started lurking around DA looking for a good online avatar to represent me, or other really cool looking art. I always kind of came back to the anthro section, because I like anthropomorphism quite a bit, and eventually I searched for "Red-Tailed Hawk" and ran across this guy. I told my roommate about my recent activities in passing, like I tend to because we both lurk different parts of the internet, you know passing news back and forth. He said something along the lines of "That sounds like a furry to me," and so I did some research, moped about for the better part of a week confused as hell, and decided that it would make an interesting hobby.
Over a decade ago I stumbled across an online chat where some furries were discussing different anthro-animal books they have found/read. I ended up following one of them to their gallery and associated myself as a furry ever since.
Eh might as well. I used to LARP (Live action roleplay for those who don't know) and as I recall I chose to be a hedgehog at the time (I was way into Sonic games back then). Since then I've delved into why I chose it and eventually came to the conclusion that deep down I like mostly everything ('Tis why I prefer Shapeshifter as my chosen fursona). And I found out about this place through a friend who showed me and I became interested in the place (But that's another tale for another thread).
Case in point: I was a LARPer and the character I chose got me on this path.
Through...actually, I have no idea how I got into it. But I really only started participating in the fandom after reading stuff on Shifti. (And by participating, I mean reading crap and drawing mediocre art.)
I've been into stuff that's sort of furry-ish as long as I can remember. Then, I started reading TF stories and later I started following some of the furry artists on DA and started following some furry and semi-furry webcomics. Then I was forced off DA, wandered the internet for a while. Then it become official when I joined FA.