I highly recommend that you read the books referred to on the previous page, but briefly, the kind of negotiation that I'm talking about isn't the kind that most people normally think of. Negotiation is often thought of as drawing a line, taking a stand, and not wavering; this is called positional negotiation. The stronger of the two sides wins. That kind of negotiation turns a chance for cooperation into a battle. The kind of negotiation that I'm talking about is called principled negotiation by Fisher and Ury. Instead of sticking to positions, you stick to these principles: separate people from the problem, focus on interests instead of positions, look at a variety of possibilities before deciding what to do, and base the results of negotiations on objective standards. Of course, the more important the outcome of the negotiation is to you, the more work you should put into it. But the basic principles stay the same.
Think again about the problem of two people who want to watch two different television shows at the same time. Instead of insisting on your getting your way, consider the possibilities. What do you really want? What does the other person really want? Maybe your initial intention was to watch a show with your child and you decided that the show that you picked was a good one for both of you. Your child probably doesn't know this and says that he'd like to watch something else. If you're willing to change your last step, there's really no problem. Watch the show that your child wants to watch and you get what you initially wanted. Often, the problem isn't that you don't want what the other person is proposing, the problem is that you're attached to your idea. Drop the attachment and the problem disappears.
As with anything else, learning to negotiate from principles isn't easy; you probably have a lifetime of habits to break. But the potential to reduce the suffering of the people involved is great. If you went through one less argument each day or even each week, how much more pleasant would life be?