Answer:
There are hundreds of rules regarding kashrut. The key points are:
* Any meat or poultry has to be certified kosher.
* Fish has to be from a kosher species, skin on. If the packaging the fish is in has kosher certification, it doesn't have to have the skin.
* Meat and dairy cannot be combined in any way, poultry qualifies as meat in this case. Even products that contain dairy byproducts (whey, etc) cannot be combined with meat.
* Fish and meat cannot be served on the same dish or at the same time.
* In North America, milk is considered acceptable by most groups. Some groups do require kosher certification for milk. Almost all require kosher certification for dairy products (cheese, etc). There is a higher level of certification for dairy products called Chalav Yisroel.
* Any processed ingredient must have kosher certification.
* Some groups do not eat certain vegetables because it's too difficult to clean them of all bugs and dirt (broccoli, cauliflower, romaine lettuce, asparagus, etc).
* Some groups require that a Jew is involved in the food preparation process of cooked food in some way, even turning on the stove/oven qualifies.
Depending on what's being served and where, some people require supervision by a mashgiach. A mashgiach is a religiously observant Jew who is well versed in the laws of kashrut.