There are a lot of theories to the big questions - many with a LOT of evidence to support them. So, rather than go through the pros and cons of them all, I'll take you through the theories I feel are most accurate, theories based on the works of some of the greatest minds on the planet, past and present.
I must point out at this point that I am no expert - I'm merely an interested amateur with a thirst for understanding; clearly you are too, or you wouldn't be here. It is important to note that we do not have all the answers at this current time. This is not to say we will not have the answers, and it certainly doesn't necessarily mean "God did it!". It could be, but we don't have proof for this yet.
For example, we don't fully understand what gravity is - but you don't hear people going "Well, duh! God personally holds us to the ground!", do you? (Unless you're a Pastafarian, obviously! But even so, the Pastafarians understand not to take things utterly seriously...)
The other side of the table of course is that, if we accept "God did it!" as our answer - well, we risk still dying of bad smells and curses! It is only by trying to find answers for ourselves that we actually find answers.
I'm also aware that some of the answers we find are highly technical - and I don't know about you, but I'm no physicist. So, I'm going to try to explain them as clearly as I am able. After all, Albert Einstein himself famously said "If you can't explain something simply, you don't know enough about it. You do not really understand something unless you can explain it to your grandmother."
So, where do we start with such diffiult questions? Well, naturally, we'll start at the beginning!
The dawn of the first day...
Batteries. In your phone, laptop, anything - a battery stores energy in a chemical format. You can then use the energy from that chemical format to emit photons (light beams), another energy format, from your computer screen. You can use it to make sound come from your speakers and some of that energy is turned into vibration by your fan...
Energy comes in lots of "flavours", each of which can be wildly different from the others.Sound is very different from light which is very different from heat. And they're just three examples, in this universe, in your "local" dimensions. They've recently proved that photons work in both wave AND particle form - imagine if water was water waves and then icecubes, all at the same time. Icecubes that flow. Kinda screwy, right?
Welcome to physics.
Someone, and I can't put my finger on whom at this moment, said something along the lines of "If it doesn't scare you a little, you're not understanding it properly." Our little bubble of universe has a big mix of flavours in it - but there could be even more that we haven't even begun to get our heads round.
Anyway, long story short, the upshot of this theory is that prior to, and around the universe, is a different flavour of energy - dimensions are just other versions of flavour, if you will.
The "bubble universe" theory starts out as a transmutation of energies - the Big Bang, some 13.7 billion years ago. Some people understand it as a fissure that spews out amazing amounts of energy - like the back end of a black hole from another dimension, if you could imagine such a thing... (Stephen Hawking does some interesting writing on the types of potential universes in "Universe in a Nutshell: http://www.hawking.org.uk/)
When that fissure originally opened, all kinds of crazy energy suddenly slammed through the hole, converting into the dimensions we're now familiar with (and the ones we ain't! Physics joke also.) and roaring out at amazing speeds. At this point, things are all kinds of crazy and all the fundamental forces are thought to be just one unified force.
Now, Mr Higgs came up with an idea for how these very first energies worked. http://www.ph.ed.ac.uk/higgs/ And just recently, CERN and the LHC found the particle Mr Higgs has been looking for, for so long.
The Higgs Boson.
I'm going to have to grossly oversimplify here. The Higgs Boson created a field, acting as the "fences" of a garden - all this energy was roaring in through the "gate", the fissure, into the garden. Like a garden party, only so many people fit in before they get squished up against the fences - the people behind have to slow down to get in, and then the fence will give way once everyone has jammed in, slowed down and is pushing against it.
I'm guessing you already know the law of states, but just in case, more energy = more excitement. Water is a great example of this: less energy, it becomes ice. More energy, it turns from solid to liquid. Hotter = turn to water, hotter = turn to gas, hotter = turn to plasma...
The fences allowed this quark-gluon plasma to slow down and cool off enough to turn into "liquid" universe, if you'll excuse a physics pun.
We end up with an amazing abundance of photons, and then a whackload of stuff that starts sticking together as it's all cramming through the "gap". The fences collapse and the matter has been expanding ever since, pushing the boundary of the universe ever outward. (You might also be interested to know that this is called the Planck epoch, zero to approximately 10-43 seconds from the event.)
We know this expansion is a fact because of a phenomenon called "microwave background radiation" (leftover heat from this early, extremely hot and dense universe) as well as "Red Shift phasing". That's also pretty tricky to explain in laymans terms - but I'll give it a go.
If you know what the "Doppler effect" is, then you can skip this point to the next set of asterisks - the Doppler effect doesn't just work on sound, it works on light, too. If you don't, please read on as normal.
"Blue" light travels very VERY fast. The "bluer" it gets, the faster and tighter the waveform.
As it happens, sound does the same thing - when something comes towards you, the soundwave gets pushed forwards, compressed, so the pitch rises. The "Nnnnnnneeeeeee" as a racecar comes roaring towards you, it always goes up in sound.
Light does the same thing, technically - as it not only behaves like particles, it also behaves like a wave.
The tighter the compression, the "bluer" the light, all the way up into ultraviolet, xrays and stuff. The wider the frequency, and the light goes red - all the way to infrared (that's heat to you) and beyond... Or "Yooooowwwwwwwnnnng!" as the pitch of the engine note from the car now hurtling away from you goes - dropping in tone.
The Red Shift properly applies to "the standard model" - the universe in "liquid" state, a few picoseconds after the beginning.
And after the beginning... came the early universe. Though it took over 400,000 years for everything to calm down enough for nuclei to capture electrons!
Once atoms started to form, the universe really started to evolve....