Sure, I'll give you my story.
I grew up in a non-believing family. My father was, and still is, staunchly atheist in a rationalistic way, with a strong belief in the explanatory powers of modern science. My mother was less certain about her beliefs, but was not active in any religion. My brother and I were not baptised as infants (causing a certain amount of eyebrow raising among the nice, Church of England, county families I come from), and my parents always told us both that they wanted us to be free to make our own decisions about what religion, if any, we wanted to follow.
I was strongly influenced by my father in many ways, and had a natural aptitude for science that I used to think was incompatible with faith. I was sent to a Catholic primary school which required a certain amount of participation in religious activities but my perception was that those of us who were not Catholics were not at all expected to actually believe any of this nonsense. I didn't think any intelligent people believed in God, and I couldn't see why you'd want to.
The first change happened for me when I went away to a boarding school where most people were at least nominally Anglican and confirmation was a normal part of the school experience. I definitely felt a sense of wanting to belong, though it wasn't until later that I understood what I wanted to belong to or why. While I was a teenager, I mainly enjoyed being contrary. In conversation with Christians, I'd argue from an atheist standpoint, and vice versa. If you'd forced me to say what I really thought, I'm not absolutely sure what I'd have said.
When I was 16 I went on a Christian summer camp for 10 days and for the first time met fun, ordinary people my age who not only called themselves Christians, but thought that should make a difference to how they lived their lives. They read the bible AND tried to obey it. Weird, or what?! But they were lovely and that really did make an impact on me.
So after a few days, someone gave a talk on the Prodigal Son, and I just knew that was me and that God was waiting for me to come home to him. No arguments, no rationalisations, just a new relationship and a new worldview which, the more I thought about it, the more it made sense of everything else.
Hope that helps a bit. Reading it through, I realise it makes it sound like I was never really a convinced atheist, but I'm pretty sure that for a while, at least, I was.