It's not a bad website in the sense that if you're a complete newbie to Chinese astrology, it tells you there are 12 animals, 10 elements (which is really a yang and yin division of 5 elements), and that Yang and Yin exist; however, to take anything more about of that website would not do well for furthering your learning in the long run.

Animals are really representatives of the "Earth's condition" at that particular moment in time. For example, The Rat is comprised entirely of Yang and Yin water. Water represents being wise, the constantly flowing nature, the dark (night), secretiveness, and even the will to carry things through (as water tends to do). Water is also related to being at the extreme Yin nature. Rat represents a coldest time of the year (because it's only comprised of water/ice/snow, whatever you fancy), coldest time of the night (absolute yin)... etc. But analysis doesn't stop there; how does the rat manifest?

Let's say the person was born on the day of the Fire Rat. Fire is Yang fire here (the self), and it's sitting on an element that controls fire (water controls fire because water kills fire). How does this manifest in the individual's personality? He would have a "controlled" demeanor, unlikely to "explode", which is the nature of Yang fire. He'd care about how he looked, be well-mannered, and act in a way that was "righteous". There's a repression of "freedom."

Let's say the person was born on the day of Earth Rat. Earth is also Yang Earth (the self), and it's sitting on an element which it controls (earth absorbs, stops flow of water). How does this manifest in the individual's personality? He would have a more "controlling" demeanor. He's sitting on an element he controls, so there's no need for him to really care about being well-mannered, be righteous, whatnot; whatever he thinks is correct would be correct.

Of course, I'm only looking at the day, and I'm only looking at elements. It is absolutely possible to do an analysis without trying to memorize the nature of the animals' personality.

For example, I think I read Ian say something about sheep keeping things to themselves. Of course, it depends on what the self element is, but if a person is Ding fire Sheep (Yin fire sheep), this is perfectly explainable through elements. Sheep is considered as "yin earth" primarily, comprised of yin fire, yin earth, and yin wood. Technically, it's an "eating god structure"; the self element sitting on an "output element" (fire leads to earth). However, sheep earth can't absorb fire well because it's already a very dry earth. When the earth can't absorb yin fire's heat, communication stalls, so the yin fire sheep individual is less likely voice his/her opinion. fire can't be translated into earth and then to metal because it's too hot for the metal to actually materialize.

On the other hand, Ding fire Ox (Yin fire ox) is the exact opposite. It also has an "eating god structure", fire sitting on earth, its output element. However, people with yin fire ox will talk up a storm. This is because ox' "primarily earth structure" is comprised of yin water, yin earth, and yin metal. It's a very cold wet earth, so the fire sitting on top of the ox is absorbed quickly by the cold wet earth full of water and metal. Communication becomes very easy, and yin fire ox individual will be able to talk about everything and anything. fire is translated into earth here, and unlike the sheep, the earth is cold, allowing the metal to materialize (because it warms up the metal instead of burn up the metal as it does in fire sheep) so it produces something visible (output), unlike the sheep which tends to keep their thoughts more in their minds.

Animals is ... a good place to start. Looking at the day animals is probably the next step; but the best place to start is the philosophy of Yang and Yin, the five elements, what they represent, their "personalities" (elements possess personalities in Chinese astrology!) and what their relationships are to other elements (and even to the same elements). It's like a big family; wood is the fire's mom, fire is the earth's mom, earth is the mom of metal, and metal is the mom of water, and then water is the wood's mom, once more. Wood is earth's husband, fire is metal's husband, Earth is water's husband, Metal is wood's husband, and Water is fire's husband. Yang fire is Yin fire's brother (or sister), sometimes a friend, sometimes a competitor. Yin wood needs the support of Yang wood to survive, and it also needs earth, fire, and water to stay alive and fruit. Water can't be just water because nothing lives in water that's too clean; it needs a bit of earth, a bit of metal, a bit of fire (so it can flow), a bit of wood so it can give life, and so on and so on.

Just the basics is very difficult, but once you really understand the basics, the more difficult aspects become much easier to understand, and you realize that animal personality is not what really make's a person's personality.

I don't think I'm nearly qualified to provide you information on compatibility.