I'm writing this with a bit of an agenda.
I spend a lot of time on Yahoo! Answers, specifically in the Religion and Spirituality section. It's a lively place, full of heated arguments. At least once a day, someone asks something about the Big Bang, typically what caused it if there was nothing before it. This is generally a tactic used to suggest a god exists who kicked the whole process into motion, though it usually sidesteps the question of where that god came from.
These questions get a lot of answers, but they generally tend to be of the 'I don't know' category, or to be generous, are a little misinformed when it comes to modern theory.
I answer, but I'm getting very tired of typing it out every single time with minor variations. If I've done this once, I've done it at least fifty times. Hence, with a certain sense of hubris, I decided to try and sum up the relevant theories in a brief article I could just link to.
Firstly, a lot of people ask what was before the Big Bang. That's a relatively easy one to answer; nothing. No matter, no energy, nothing but nothing. Not even a vacuum. There wasn't even any space for something to occupy, no time for it to exist in. There wasn't a before, before.
So what led from this nothing to, well, everything? The original Big Bang suggested that everything, every single piece of matter that now exists, was originally scrunched up into a point so small it stops having any dimensions at all, a singularity. In cases like this, some suggested all that matter came from a previous, collapsed universe.
Nowadays, scientists use terms like 'a quantum fluctuation resulting in a particle of negative pressure vacuum energy'. Which to me sounds like something from Star Trek, but apparently it's perfectly acceptable to allow the universe to spontaneously generate in this way, and it's backed up by empirical tests. Either way, you now have your singularity; either a zero-event point containing everything, or one containing nothing. Your mileage may vary, but not by as much as you'd imagine.
At this point, you stand well back. Do not attempt to return to a lit singularity. Within a fraction of a second that's too small for the human mind to begin to envision comfortably, there's a blinding flash, and an outrushing of a staggering size and velocity. In this instant, the building blocks of energy, gravity, space and time are flung out. Temperatures are around 10 billion degrees celsius. As it expands, things start to gradually cool down, cohering into subelementary particles, and eventually matter. Within three minutes, the light show is over its spectacular stage, and 98% of the matter that will ever exist, exists.
After all the excitement, it's merely a matter of waiting for things to settle down, and waiting for all the helium and hydrogen to clump together into stars, which in turn eventually supernova and produce just about every heavy element above lithium on the periodic table, which then begin to form new star systems with actual planets. It's all a bit Newtonian by this point, and not nearly as exciting to watch; if you wait around about eleven and a half billion years, important things like tea and sponge cake and pocket-sprung mattresses find ways to come into being. Oh, and life, also.
There's a lot of evidence to back up the theories behind the big bang so far. Perhaps most notably, the background radiation from the event itself, which fills the night sky in all directions, and reaches the earth in the form of redshifted microwave radiation. You've all actually witnessed this; if you turn on a TV and tune it to a dead station, about 1% of the hissing static you see will be these microwaves. As Bill Bryson says, if you ever complain there's nothing on TV, you can always sit and watch the birth of the universe.
There's also a lot of minor inconsistencies in the theory, which will only get a brief mention because frankly, they're way too scientific. Scientists are still working out the fine details and adding to the theory; it's all rather cutting edge considering it's talking about something which happened so long ago.
And there you have it. A reasonable explanation as to how everything came about without anyone having to poke it to make sure it works, or say 'let there be light'. It's quite possible a supreme being could do exactly the same and create the singularity needed, but there's no necessity for there to be such a being.
I'll not quote any specific sources for all this. To be honest, most of it is rather boring, horribly technical and long winded. If you're interested, searching Wikipedia for 'Inflationary Universe' and 'Big Bang' will provide you a couple of lengthy articles with lots of Science with a capital S; the hows, whys, wherefores and possible problems with the theory. If you're interested but not to the point of doing a degree in physics, I'd recommend Bill Bryson's 'A Short History of Nearly Everything', which covers it all (and a lot of other things) in a well written, easy to understand, and humorous way.