I'm an atheist who is an atheist as a consequence of where science leads me - my atheism is a working conclusion rather than a presupposition, and certainly not a faith. I'm occasionally asked how I get to that point, so this is where it starts.
I like to take the track credited to Descartes and his Cogito - I think therefore I am; or, if I'm thinking I can only conclude that something is doing the thinking, and that something I'll call 'me'. I'm not claiming this as a proof that I exist, but I am saying that it is the only evidence available to me that I exist. Feel free to criticise this; but it would be helpful if you could provide an alternative that is as all invasive as the experience that I am having of thinking.
I'm not sure what it would mean, what the consequences would be, if I were to say I am thinking but it's not me, it's something else thinking these thoughts, or, that my thoughts are an illusion (but what is it that is having the illusion of thinking), or that there is no thinking going on full stop.
So, based on this thinking experience, I accept the experience that is 'thinking', i.e. I think. I've had some people tell me this is my presupposition, but I don't think it is, I think it's a direct experience that I can't refute.
Next I notice some senses, some apparent external inputs from some apparent external world - I see objects and people, I hear them, they appear to respond when I talk to them. Is this a phantom world created by my mind? Is there only thinking? This solipsism is a distinct possibility, I can't deny it. Trouble is I can't for the life of me tell the difference between the solipsism of imagined senses and real actual senses. Since that's the case I'll continue from here by choosing the arbitrary path - that my senses are real inputs from the external world, external to my thoughts. It's important to realise that this is an arbitrary choice because I can't tell the difference, I can't refute solipsism.
Form there, through these senses, imaginary or real, I accept the discovery of other people who appear, according to my senses, to have the same experiences - at least that's what they tell me. Not being able to refute any of this my basic working model, my working philosophy, is that we all exist and interact as our senses show us and our cognition (mind) understands us. This experienced world is the one we know as the physical world, or natural world, that applies to all of us.
At this point we can't say to what extent our mind and senses report on the real, actual, universal, ultimate reality (or whatever you want to call it) that's out there. We can't even be sure there is such a thing. So note again the contingency of our position: we only think that we have a mind, and with this thinking mind we think that we have senses, but can't be certain, and if we do have senses we think that they show us something of reality, but we're not sure, and we don't even know if this reality exists. But despite how contingent, how flaky and inadequate this position is that we're in, it's all we've got!
Next, I want to cover how humans deal with thinking about stuff in the light of these limitations.
 Cogito - Note I don't consider too many of the options that Descartes does, because I can't figure out what to do with them. And since nobody else takes us any further than this I am left to take from it what I've stated above.