Capitalism is inherently more complex than communism. While communism is perforce a monolithic structure, centrally managed and as simple as possible, capitalism is based on a few simple ideas that allow so much freedom that pretty much anything can happen (and usually does). Explaining it therefore requires us to start at base principles and work outwards, exploring the ramifications as we go.
You can pry our freedom from our cold dead hands
The base principles of capitalism are freedom and ownership. Freedom means that nobody else is allowed to tell you what to do with yourself. Ownership means that nobody else is allowed to tell you what to do with your possessions. Most libertarians maintain that the latter flows from the former, but they are in fact two separate rights. However, you cannot have control over your possessions without control over yourself, so ownership is dependent on freedom.
Private ownership leads to trade
Private ownership of property includes the right to freely exchange that property with others. Freely, in this case, meaning the right to decide how much of what you have you're willing to exchange for an agreed amount of what someone else has (for example, the right to say that you will exchange your sheep for two of your neighbour's goats).
Trade leads to currency
At some point it becomes obvious that a sheep isn't actually worth exactly two goats, it's worth nearer one and a half goats, or possibly one goat and 3 small clay pots. At this point it generally becomes necessary to invent 'currency' and decide that a sheep is worth £200, a goat is worth £130 and a clay pot is worth £20. Of course it's not as simple as that (see WhatsItWorth?
Now, the advantage of capitalism in its most basic form is that what you work for is yours. Whether you're raising goats, growing crops, mining or building houses, the end result belongs to you, and the harder you work, the more you get. While this is a lovely theory, it doesn't quite work.
Luck and judgement
Firstly, no matter how good you are, everyone has bad luck from time to time. You can be the world's best goat-herder but when an avalanche wipes out your flock you're still left with nothing at all for all your hard work. While this is an extreme example, almost any work involves some luck, whether it's stumbling over some very fertile land, building a house that catches a fashion or digging a mine straight onto diamonds as big as your head.
The Upward Spiral
Of course, once you have money it becomes easier to make money. If it takes a certain flat amount of resources just to survive, then having slightly more gives you a small cushion from a bad crop year. Having twice that much means that events that wipe out your neighbours leave you intact. Having vastly more means that you can buy the better farmland or the best goats and make a long term investment. If you have no money you can't look to the long-term, you can only struggle to survive from moment to moment. Obviously, the people that can afford to plan long-term will be more successful, thus leaving them with even more money.
In these enlightened times, of course, people aren't actually ownable. But ...they are rentable. And for people who don't have their own goats, the chance to be paid to raise someone else's goats is too good to pass up. Of course, you don't make as much out of it as you would if they were your own goats, but on the other hand a harsh winter won't finish you off - so long as your employer is around, so will you be. And if your employer doesn't survive then there are bound to be other people around who value a man who can herd goats.
=== A class of your own===
So a mixture of luck and hard work splits people into those who own the goats (or other means of production) and those who actually herd the goats (or do the producing). Those of you unlucky enough to have been forced through a sociology course will have recognized the words "means of production", but don't worry, this isn't going to turn into "An introduction to Marxism". It is, however, worth pointing out that these are the two classic "classes" in his Class War. The split wouldn't be too unreasonable over the short term, after all hard work (and intelligence) generally has a large effect on a person's output, so it makes sense that those that do better in a capitalist society should be the ones who both get the rewards and manage other people (who obviously couldn't manage themselves, or they'd have done well too).
We are not all created equal
The problem is that the split isn't just short term. If you're a child of the rich then you get the best of everything. Better food, shelter and entertainment are all there for the picking, but far more importantly, better education is your birthright. Studies have shown that the difference in IQ (an imperfect measure but still a useful pointer in some ways) between two generations of the same family, one of which could afford education, is up to 30 points. This alone is enough to cause the class split to become near-permanent.
Looking after yourself
It's a standard capitalist position to hold that people should be entirely responsible for themselves. It's a person's responsibility to buy health insurance so that if they fall ill they are looked after without others having to pay for their care. If a person wants to be educated then they should save for it. Nobody has to pay for another's welfare, because nobody has any right to tell another person what they should do with their own private property.
But what about the children?
A less arguable position would be to state that the children of poor people are responsible for their own care. It is certainly not the fault of the child that their parents aren't able to afford health insurance for them. Nor can it be said to be their fault that they can't afford to be educated. To make children pay for the failures of their parents seems illogical. When their parent's failure may well be based on _their_ parent's failure then it's madness to carry on a near-infinite chain of poverty and low achievement.
More to Come