As an opener I'd like to state that my worldview has absolutely nothing to do with my atheism. I like to think that were I a theist I would still hold life, the universe, and everything in exactly the same regards. This post is not intended to answer any questions about nor explain my view on theism. Correlation does not imply causation. That being said, let us proceed.
Where did we come from? Four billion years ago or so, just the right combination of chemicals came together somewhere on this planet. Some phosphates, some sugar and nucleobase molecules, and a charge of electricity or radiation (lightning?) have been proven to be all it takes to create life. It's hardly "something from nothing," but as uncommon as it is, given a lot of chemicals and a lot of lightning and billions of years something's bound to happen. Those are the layman's terms, of course; I'm not a chemist, a biologist, or a physicist. But there's proof, so there you go. It may not be the correct answer, but it's the best one out there yet and it's certainly more realistic and preferable than "God did it" (which would only raise more questions).
Of course the life created was the simplest it could possibly be. On a relatively new planet, however, given plenty of time and a fast-changing environment, this life began to change. It evolved, more cells began to work together, organisms formed, they grew fins, swam, poked their heads out of water and began breathing air, crawled onto land, grew legs, scales, feathers, wings, fur (not necessarily in that order) and, billions of years later, here we are. That was the condensed version. Be sure to research natural selection to learn more about how all that busy stuff actually happened.
Why are we here? This is still up for interpretation. Taken to mean "what is our purpose," one could say that as a species our only purpose is to continue to propagate the species. Man find woman. Man court woman. Woman bear child. Child grow up. Find mate. And so on, and so forth.
If you're looking for a deeper purpose, I could only tell you my own as I believe every person finds his or her own purpose in life. Mine is to be happy and have a happy family (first) and try to keep everybody else happy to my best extent (second). This includes going to school, getting a job, telling jokes, writing songs, singing loudly, smiling a lot, dancing when the mood strikes me, wearing comfortable shoes, playing video games, keeping a blog, donating to charities I know will make the world a little easier to live in for some people less fortunate than I am. If you think my purpose is anything more or less than that, then I'm so very sorry for not living up to your standards. I apologize if my purpose seems a little superficial compared to yours. The fact of the matter is that I'm happy, my family is happy, and ain't nothin' gonna bring me down.
Where are we going? This one's easy. Eventually, as happens with all species, the human race will go extinct. It may or may not be replaced by another sentient race, more adaptable to change and more capable of surviving in whatever the conditions are at the time. I doubt very much that we will be the last animal to go extinct. In the end, nothing we say or do or accomplish as a race will matter. Not to us, at least; we'll be dead. It very likely will matter to whatever species outlive us, since there is no doubt we will have changed our planet (whether it's earth or some other planet we move on to in the future) in a manner that will affect the other animals around us. Knowing that, maybe we should try and keep things nice and tidy 'til we go.
In terms of where each one of us goes, or how we end up, being that I don't believe in any afterlife (primarily because I have no reason to) we'll just die. That'll be it. Physically, our bodies will decay and nourish the land and life around them. Metaphysically, one must remember the human is a social animal. We tell tales, sing songs, and create art. Not that it'll matter to me much after the fact (since I'll be dead), but I like to think here and now that once I've died I'll be remembered. Perhaps people will still listen to the music I've created or read the stories I've written. That line of thinking - that I'll possibly be remembered in those ways - brings me comfort and makes me happy. See "Why are we here?" above if you've forgotten why I think that's important.
Why is goodness good, and what are morals anyway? Who am I to say what's good and right versus what's bad and wrong, you might be asking. I'm not a philosopher so you'll have to forgive me if you disagree, but I prefer to take the utilitarian route and define goodness as whatever makes the greatest number of people happy and comfortable, and causes the least amount of discomfort, pain, or unhappiness. That answers, as far as I and my opinions are concerned, the question of why it is good to be good.
The less important question here is what are morals and where do they come from? I, the non-philosopher, prefer to ask who cares? Morals exist. Everybody has a different view, and some of them contrast with one another, but how we developed morality is completely irrelevant. It is, though, also completely answerable. I already mentioned humans are social animals, but I need to bring it up again here because it's pretty important. At some point in our ancient history of evolution we discovered that is it more beneficial to work together to accomplish a particular task, as opposed to going it alone. As family groups became more common, we realized it would be detrimental to our well-being if we killed or hurt those around us. Anybody who did so became an outcast as they were seen to be harmful for the future of the family/clan/community. For (hopefully) a better understanding of how we may have developed morality and ethics, I will refer you to the parable of Grog and Zog - a silly name for a story about cavemen that teaches an important lesson.
Still have questions? Read it again.