Joab, to answer your question it was a process of stepping back to honestly consider the possibility that everything I had been taught to interpret as evidence for the existence of god (burning in the bosom, inspiration through prayer, miracles, etc.) might be explained as coming from natural sources. I had very deep, personal feelings of commitment, communication, and what I considered a real relationship with Christ, but honesty required me to admit many years later that this may have all come from within.
As a psychologist, I understood how our beliefs, emotions, and thoughts can be subliminally generated by the brain. None of my experiences had to come from a supernatural source. I realized that some of my most deeply cherished beliefs, which I knew to be true through inspiration of the Holy Spirit, were factually impossible once I did objective research on my faith. I won't get into details on any of that here, except to say it was a very sincere process of documenting the best evidence I could find on both sides of the argument, and honestly considering the conclusions required by the evidence.
I also realized that people of different faiths can be equally sincere, equally convinced that god has spoken to them, equally born again, and equally accepting of Jesus as their Savior, yet their conclusions based on what god has told them contradict those of other faiths. Logically, it is impossible for them all to be correct, so it calls into question this whole process of inspiration and the conclusions we draw from that inspiration. I now believe those conclusions, however sincere, are derived from entirely natural processes and are not proof of the divine.
Not to say this disproves the possibility of god(s). It's impossible to prove something doesn't exist, so honesty requires admitting the possibility, however remote. However, lacking any reliable objective evidence, I think it is similarly dishonest to draw conclusions that something exists when in fact there is no real proof that it does.