A good way of thinking about this question is to ask yourself what the world would be like if everyone, at all times, treated other people the way they themselves would want to be treated. It's a fair assumption that most people want to be treated with kindness, consideration, courtesy, and respect. Surely, then, if people applied the same standards to others as they do to themselves, the world would be a much better place for it.

Then, we'd be in the happy situation where people would be treating each other as ends in themselves, not as means to some other end. In other words, we'd act towards others not for selfish reasons, not for what we could get out of it, but because other people are inherently deserving of respect simply by virtue of their humanity.

Simply put, this means you should treat others the way you would like to be treated. If you don't want to be hurt, treated unfairly, or ridiculed, don't do those things to other people. This is called the Golden Rule and is central to most religious faiths.

Conflict resolution mediators practice a version of the Golden Rule. If a dispute arises over, say, proper distribution of mineral rights, the mediators will have the parties in the conflict sit down and draw up what they think is an equitable division of the rights, without knowing which half they will get. When people don't know what portion will be theirs, they tend to be fair.

We never know where might end up in life. We may be riding high and think we will never need help. But anything could happen. If we live by the Golden Rule, we will treat people who have bad luck as kindly as we would like to be treated if it were us. If this becomes a social norm, we can rest easy knowing we too will be treated with compassion in bad circumstances.

To put it into different words, "do unto others as you would have done unto you," means that one should treat others as one wants to be treated. Obviously, we all want to be treated well, right? If one does not want to be picked on or bullied, alienated, or ostracized, one should not pick on, bully, alienate, or ostracize anyone else. Theoretically, this would work to create a pattern of good will: if I treat you well because that is how I want to be treated, then that will put you in a good mood, so you are more likely to treat your friend well, and that will put him in a good mood, and he will treat his sister well, and so on and so forth. Even if it does not work out this way, then I have still behaved in a good and moral way, and I can feel good about that. It is almost like saying: no matter how anyone else treats you, you can still do right and treat them well.

The simplest way to explain the Golden Rule is that if you want to be treated well in this world, you should treat others well. If everyone follows this philosophy, everyone will treat others well and therefore, everyone will be treated well. 

Another logical proposition that derives from the Golden Rule is that we are more likely to enjoy life if we contribute good deeds rather than bad actions. First, we get the social, psychological, and spiritual comfort of having done something good for other people. Second, because we contribute good things to the world, we make the world better. And since we live in the world, by contributing good things, we are directly making our experience in that world better.

We all live in the world; we all participate in life. Consider the analogy that we all drink from the same spring. If we add bad things (pollutants), we are making the water bad for everyone, including ourselves. If we add good things, we are making the water (analogously, life) better for ourselves and others.

It makes moral and logical sense to do good to and for others because we're making the world better for them and us. There is the general idea here that "everything affects everything." Think of Newton's Third Law: 

For every action there is an opposite and equal reaction. 

In human society, good actions tend to lead to other good actions; not the opposite evil actions. Newton was talking about force. In this context of morality, we're talking about humanity. Speaking of the Golden Rule, Newton's Law could be rephrased like this: For every good action, a subsequent good action is more likely to occur than a bad one. I not only reinforce my own good behavior; I also make others happy and therefore increase their likelihood to be good to others (including myself).