Edit 14 June 09: I'm considering purging this post. There's some good philosophy going on in there somewhere, but it is not well-argued. I'll probably rewrite it as a sequence of posts at some point.
The basic principle of modern skepticism is that it's not about what you believe, it's about why. A good decision made for bad reasons is an oxymoron: flukes don't count.
Of course, this is not a complete answer. How do you know if your reasons for believing are good? For a start, you can look at how different approaches have panned out in the past...
In some areas, this is pretty much a solved problem. As far as figuring out how e.g. fundamental physical objects interact, it's a gimme: the scientific method as applied to physics is where it's at. Similarly for chemistry, cosmology and basic biology. By following the scientific method, you can analyse, understand and, most importantly, predict. The end justifies the means.
So what are the limitations of this method? What are the pathological situations where it breaks down? My favourite example is poker. By definition it's impossible to predict the responses of a good poker player: if they were predictable, they wouldn't be any good. The scientific method breaks down when someone is actively trying to subvert your results, which is why many excellent scientists get badly suckered by psychics.
And yet, in many ways, this is the area where understanding is most important to us. We live in a world constructed almost in its entirety by other people, none of whom would feel terribly comfortable if they thought we fully understood them. The man who understands you can manipulate you, can use you for his own ends. Attempting to understand someone borders on the disrespectful, and people will resist it tooth and nail.
The extent of this effect can be demonstrated by looking at the quite frankly convoluted procedures psychologists have to use. To get useful results from a subject, the good psychologist will have to thoroughly deceive that subject about the goal of the experiment. If you're doing an experiment about attention spans, tell them it's about pattern recognition. If you're doing pattern recognition, tell them it's about political reactions. Otherwise your data will be hopelessly contaminated by your subject's second-guessing of their own behaviour.
So how can we understand another person well enough to e.g. date effectively? There are two basic approaches: the theoretical and the practical.
The theoretical approach tries to achieve an understanding of your date that's one level deeper than your date expects. This approach is well known by stage magicians: by planning one step further ahead than your audience expects, you can create the most magical effects.
One example that I like was provided by my sister. When she was younger, a number of her friends were big fans of the horoscopes in the local paper. So if she was on the out with a friend, and that friend's horoscope said "a person wearing blue will be important to you today", my sister would wear blue. By understanding the factors that influenced her friend, she could achieve a closer relationship.
In dating, a similar role is played by the modern romance. Human beings are strongly conditioned by films and books to expect certain things of each other. This doesn't always work out well for us as a species. It's noticeable that the heros from action movies would have real trouble with the heroines from romantic films. So when an action-loving bloke meets a romance-loving girl (or vice versa) there are likely to be fireworks. And not in a good way.
The way to get round this is exactly what you'd expect: watch lots of sloppy romance films. This is a real issue for me - I'm a hide-behind-the-sofa kind of guy when it comes to this sort of thing. I empathise with the characters far too much to watch them blithely making fools of themselves in this way. I can't stand Mr Bean either.
But in the interests of fostering better communications between the sexes, I'm willing to make the effort. I just watched my first romantic comedy in years: the film Hitch, with Will Smith playing a relationship coach. I can't say I enjoyed it - in fact I spent most of it clutching my head and yelling at the screen "no! You idiot! Don't do that!!!" But I feel I've grown as a person. Soon I hope to be able to view stuff like this without needing heavy doses of anaesthetising whisky first.
Oh, and the practical approach to dating? That's to just try it a few times and see what works. In the end, this really is the only way of getting anywhere with something as complex as a woman...