It was a gradual journey for me, and happened simultaneously with my initial walking up from JWism. By the time I was enough beyond the grasp of the cult to investigate it online, I was already an atheist. The funny thing is that I might've held onto a belief in good longer if not for the scathing review of christendom that I was raised with in the cult. I grew up heating constantly of the dishonesty and hipocracy of other religions, and long ago decided that I would never be a part of anything like that.
As I got older I became interested in science, and especially physics. This led me to learn a lot about cosmology, which led me feeling that it is just as likely that the universe could've come about without a god as with one. This kinda led me back to the question I asked as a child that never got a satisfactory answer: If the complexity of creation is proof that it was created by an intelligent designer, wouldn't that designer, in turn, need a designer? (I'll about I was probably less articulate when I asked my mother a variation of this question when I was about 8). It always felt hypocritical to me that we would ridicule scientists for a lack of understanding of what came prior to the big bang, but we ourselves responded with some variation of "it's not for us to know" when asked where god came from.
At the same time, I was learning about evolution and found that it explained things so elegantly (and predicted many things that were only observed later). Again, god was not necessary for any of it. Archeological evidence that humans had existed for well beyond 6000 years also had no refutation in the WTS publications. There was a period where I actually eagerly awaited an article that explained how carbon dating was flawed, this would've left me with that feeling I had in my childhood that I knew something these so called experts didn't. Oh how I had loved that feeling I got when I could don a superior attitude and explain to someone how Christmas was pagan or how mammoths where found with clover frozen in their bellies (which, somehow, was evidence for a global flood). Strangely, no article refuting carbon dating was ever published.
I also observed many other religious people making obviously flawed arguments for their personal interpretation of creation (particularly young earth creationists) and resolved never to tolerate such an argument, regardless of where it came from. Examining my own beliefs under this lens left me most of the way to atheism. In this stage, when confronted with anything regarding other religions, I often thought to myself, "if I wasn't a jw, I'd definitely be an atheist."
I was still left with years of indoctrination about the bible, that it must've been from god because of its scientific accuracy and fulfilled prophesy. I started with the scientific accuracy bit and this part seemed to boil down to a few things that I'm sure will be familiar. The commandment to the Israelites to bury their poop, the "circle of the earth" bit, and the water cycle description. Upon objective consideration, I found none of these to be evidence of special knowledge bestowed only upon Jehovah's servants. This left me with bible prophesy as the last bit of evidence for god. Upon objective observation, I found that the only prophesy that could not be explained without the supernatural was a few of the prophecies in the book of Daniel. A little research left me with the realization that the argument that the WTS always so vehemently fought against, actually had a lot of evidence behind it. Daniel was written after the events it professed to foretell.
At this point I was in the of position of being absolutely sure that atheists has it right, while still refusing to believe that I (and my parents, who I always considered to be quite intelligent) had been systematically lied to and fooled all our lives. After a period of soul searching I resolved that God would forgive me for checking out apostate sites of it was with honest motives to know the truth. About 3 days, and every article on jwfacts and a good bit of jwsurvey and others, I was finally free of any notion that god was out there.
So to make a long sorry short, it was a journey of nearly 20 years, starting before my teens. Since it was so slow, I did have the advantage of being able to consider a lot of the things that often seem to trouble people as the consider the possibility that there is no good or afterlife. I decided I was OK living this life the best that I could, and if that's all I got, then it was more than I deserved. After all I had done nothing to earn my birth. I considered morality without a god before I was sure of his absence. When I woke up to the lies of the cult, while still a shock, I suspect it had less of an impact on me than those who find themselves simultaneously questioning the cult and the very existence of god.
Holy crap, that was long. Sorry for the wall of words.