To get Kosher meat takes three main steps: choosing the right animal, killing it in the proper way, and removing non-kosher parts from it. (This is all an oversimplification, of course.)
- Choosing the right animal
Kosher land mammals are those who chew their cud and have split hooves. Kosher birds are those that aren't one of the ones listed as not kosher in the Bible. Note some avoid species of birds that we don't have a tradition are kosher, lest they be one of the non-kosher ones. Kosher fish have fins and scales. Kosher locusts...well, who wants to eat those anyway? Oh, and the animals can't be terminally ill; for certain species that often have issues in this regard, a post-mortem inspection is performed.
- Killing it in the proper way
Fish and locusts can be killed in any way. Mammals and birds are killed by slicing the throat with a sharp, perfectly non-serrated knife using a slicing motion not a chopping motion. This is done by Jews who are experts trained in the specifics of the laws of slaughtering, known as Shochtim. A short blessing is recited prior to killing the animal as before all Mitzvot, but it is not an essential part of the process.
- Removing non-kosher parts from it
There are three parts of an animal which may be non-kosher. In birds and land mammals, the blood is not kosher so it is drained, and further removed by salting the meat to draw out the blood. In land mammals, the sciatic nerves are not kosher. In domesticated land mammals, certain fats in the rear of the animal are not kosher as well. These last two problems can be removed, but it takes a lot of time and effort so in countries with a sizable non-kosher meat market, the back half of domesticated mammals is often just sold away.
For everything else, bon appétit!