For me, it was largely a matter of finally having a good reason to do the research. I was a barely-active JW who only stayed in because I didn't know anything else. I liked a lot about the religion but the social aspects of the religion were discouraging and hard for me. I simply pissed away my twenties because I didn't think I had any good reason to try to do anything with my life if this system was temporary.
I'd been staying away from apostate info for years, although I didn't fear it, I just thought it was not going to tell me anything that (a) I didn't know and (b) was able to be confirmed. I was already well aware of things like 1975, Russell's mysticism, and various organizational issues, but I still believed it was God's imperfect channel. But more than anything I just didn't have a reason to want to leave.
Finally I had a once-in-a-lifetime opportunity come up in my life and I realized that if I wanted to keep being a good Witness (note that I'm not saying "a good person", just "a good Witness"), I would not be able to act upon the opportunity. So it occurred to me that it would be stupid to keep letting life pass me by and not research my religion with all available information. I delayed the inevitable because the prospect of having to leave everything I knew was a bit frightening, but in the next year, I gradually stopped slumbering through life and began reading web sites.
I don't know how I found JWfacts, but it was the main avenue of TTATT for me. I remember reading a few articles and not being totally convinced. Then I got to the one about the organ transplant ban. I thought, "Okay, I have to see this for myself." I read the original QFRs on my Library CD-ROM which started and ended the ban, and I remember clearly thinking, "Well, that's it then. There's no way this can be the truth. This can't even be a highly-imperfect-but-God-chosen organization. He simply would not allow his shepherds to mislead the flock and cause them to die over such stupid misunderstandings of scripture."