Hi Masterwolf,
First off, there are certain animals which are kosher to eat (if slaughtered properly) and ones that are not permissible to eat. Jews are allowed to eat beef, chicken and fish with fins and scales, such as tuna, yellowtail, salmon, cod mackerel red snapper, striped bass, sole, bluefish, etc. (Now I'm sure I've left some animals out, but others can fill in what I left out.) For cows, it's because they chew their own cud, and it's something to do with cloven hoofs. Furthermore any animal that is a predator is unkosher. Shellfish is definitely not kosher because of the lack of fins and scales.
Then there's the issue of not mixing meat, and chicken with dairy. That comes from part of the Bible (I forget exactly where) which says "You shall not seethe a kid in it's mother's milk." The idea is that life and death are separate. Milk signifies life, and blood signifies death, and we don't mix the two.
Now for the slaughter. The laws of Kashrut are such that the animal must be slaughtered in the most humane manner possible. That means making a few small cuts in it's throat, with a special kind of knife that is extremely sharp, so that the death is as fast as possible. The Talmud provides specific instructions on how the knife should be shaped. On a side note hunting is prohitibed, as it is cruel to the animals, and any animal killed by a hunter is unkosher for that very reason. Furthermore, Jews may not slaughter an animal in front of it's mother or on the same day as the mother is slaughtered. Also, if the animal escapes, you are not allowed to go after it.
After the animal is slaughtered the next course of action is to check the internal organs. If they appear to be abnormal or look diseased, then the animal is still not kosher. On the other hand, if everything looks good, the animal is OK to cook. But before that, we remove all traces of blood and veins, by rinsing in water and salting, as the blood contains the soul of the animal.
A month of two ago, one of the members here put up a link to a speech given by Rabbi Tovia Singer about the Talmud. However, it might be worth listening to just to hear the Rabbi's experience when he went to a slaughterhouse as a young rabbinical student. If I find the link, I'll send it to you if you like.
Now if you're asking about specific cuisines, they vary depending on regions/countries. Some common kosher foods are gefilte fish, and matzoh ball soup. But there's lots more.