In my youth, I was quite the sailor. I took sailing classes and spent a fair amount of time out on the water hauling in sheets, manning tillers, and yelling things like "ready about!"
One of the first things you learn about seamanship is you never trust any of your instruments. You only start trusting what they tell you when a few different instruments give you the same information. These days, we have many different means at our disposal for plotting where we currently are out on the water - some high-tech, some low-tech. Good sailers use all of them to establish a "consensus" of their location.
The key point here is that good sailors think probabilistically. They are never 100% certain of their measurements, but as they gather more and more data that provides the same information they become more certain of their predictions. Certain enough to navigate by. They also update their beliefs based on the accumulation of more evidence. In probability theory this is known as Bayes' Law and has been successfully applied to an incredibly wide range of fields from engineering to economics to medicine to law. It has recently enjoyed a bit of the limelight thanks to Nate Silver's incredibly (one might be tempted to say 'spookily') accurate prediction of the 2012 United States Presidential election.
When I mention to people that I don't believe in a god I usually get some sort of comment/question along the lines of "But how can you know?" And the truth is I don't know. No atheist knows - and no serious atheist will claim to know (after all, that would be claiming supernatural knowledge and we tend to frown on that!) Socrates says it well:
But more and more instruments are providing more and more information that suggests with ever increasing probability that we live in a universe with no god. All of the following points are huge topics and I'll probably end up writing extensively about all of them, but here's the quick version:
Scientific inquiry continues to reveal truths about the cosmos that render god, especially a personal intervening god, utterly superfluous. Physics, from Newtonian models to Einstein's general relativity, to quantum mechanics and the standard model, describes a Universe that operates independent of any supernatural entity. Genetics and evolution provide context and evidence of the emergent complexity of life on our planet. As we continue to establish a universe that doesn't require a creator, a simple slice of Occham's Razor does away with the whole idea - or at the very least shifts the burden of proof squarely onto the theists.
At the same time, the interdisciplinary efforts of anthropology, psychology and neurobiology are providing explanations for the development of our moral landscape that are both more coherent and more satisfying than an old man talking to a bush. And a modern study of comparative religion and history provides a satisfying and entirely secular explanation of why we humans developed religion from mysticism in the first place. Incidentally, it also provides an understanding of how all religions fade and die, something I take great comfort in. Richard Dawkins put it best:
When it comes to ennobling human existence through Truth, religion is left with an ever shrinking piece of the pie. Some theists point to certain questions that science hasn't answered yet as justification for their beliefs. This "god of the gaps" argument is inherently flawed (it's the old "argument from ignorance" fallacy) and is rejected by serious Theists. Some profess that their faith should be held as more impressive and virtuous because they continue to cling to it in the face of better explanations. This rejection of reason and stubborn refusal to change and grow is an act of intellectual sabotage. Finally, some believers fall back on the odious drivel of Pascal's Wager - the argument that in the absence of proof one way or the other, we should hedge our bets by professing belief - if there is a god we "win" and if there isn't a god then we haven't lost anything. This is, at best, an extremely anemic profession of faith and at worst abject cowardice.
What about Spirituality? One needn't rely on religion for numenic experiences - I consider myself to have an incredibly rich spiritual life without the benefit of a cosmic wizard pulling the strings. Finally, to those who profess belief out of a desire to leave room for some "Mystery" in the Universe, I'd suggest you read up on some science. There are more beautiful mysteries to be found there than in any holy book. The Universe is full of wonder, beauty, mystery, and Truth just as it is - supernatural puffery inevitably cheapens - Hitchens would say 'poisons' - everything.