For me it just happened without me realising it.
The first step happened when I discovered the lies and deception of the watchtower (which also came about by accident). I was actually googling to try and find if there were any stories from gay jw's trying to find out how they dealt with life as a jw. I clicked on a story on the JWFacts website. Once I read the story, I deleted rest of the URL and went to the home page. Growing up I had a lot of questions that never got a satisfactory answer and there were a lot articles throughout the years that I just didn't agree with (eg. their view of rape). So I read through the website, seeing all the flip flops, the quotes from the various watchtowers over the years, which quite a few I remembered. I found it funny that I didn't even notice the flip flops within the teachings even into my 30's. But seeing it right in front of me, I couldn't deny the truth about them. I'd stopped going to meetings nearly 2 years earlier, but after 2 hours from reading the story on JWFacts, I was now and ex-jw both physically and mentally.
I went to a website call talkorigins.org. Wanted to read a bit about evolution, as I never paid attention in school in science because of jw beliefs. On that website I found articles relating to the biblical claim of a global flood. Geologists shoot that down in seconds. That got me thinking then about the other claims in the bible. Up until this point I'd kept researching online holding onto a belief in a god, trying to find proof that he exists.
I'd always just taken the orgs word on the bible's origins and who wrote it. Well, anyone who has honestly researched the bible and it's claims, knows the rest. The bible equals bullshit. About as factual as Gone with the Wind. Outside of the bible there is no evidence for a god, just what people want to attribute to a god. Growing up I was fascinated by ancient greek and egyptian gods and mythology and now there was one more god to add to the realm of mythology. I wasn't even sad or angry at losing my belief in the christian god or jesus. I'd held on to belief as long as I could, but I could no longer deny the evidence to the contrary.
All the questions I had growing up in the org have been answered and it is such a weight off my shoulders. I still hear christians ask about where life came from (you know, the last straw they have to clutch at when everything else they claim gets refuted), and my truth to that question is, "personally, I couldn't care less how life began". I will leave that answer up to scientists and just live my life the best I can. If the answer comes in my lifetime, great, if not, my life will not be affected one bit.
I never even recall hearing the word atheist until after I became one.