The origins for keeping kosher can be found in several Biblical sources. However, those who may say that the Bible should be taken literally without any interpretation would never be able to figure out how to keep kosher without the interpretation and elaborations given by the rabbis. For example, part of the laws of keeping kosher include separating meat and milk products (i.e. no cheeseburgers allowed). However, the Torah's reference to this idea is "don't cook a young goat in it's mother's milk."

Biblical sources are as follows:

Of the "beasts of the earth" (which basically refers to land mammals with the exception of swarming rodents), you may eat any animal that has cloven hooves and chews its cud. Lev. 11:3; Deut. 14:6. Any land mammal that does not have both of these qualities is forbidden. The Torah specifies that the camel, the rock badger, the hare and the pig are not kosher because each lacks one of these two qualifications. Sheep, cattle, goats and deer are kosher.

Of the things that are in the waters, you may eat anything that has fins and scales. Lev. 11:9; Deut. 14:9. Thus, shellfish such as lobsters, oysters, shrimp, clams and crabs are all forbidden. Fish like tuna, carp, salmon and herring are all permitted.

For birds, the criteria is less clear. The Torah lists forbidden birds (Lev. 11:13-19; Deut. 14:11-18), but does not specify why these particular birds are forbidden. All of the birds on the list are birds of prey or scavengers, thus the rabbis inferred that this was the basis for the distinction. Other birds are permitted, such as chicken, geese, ducks and turkeys.

Of the "winged swarming things" (winged insects), a few are specifically permitted (Lev. 11:22), but the Sages are no longer certain which ones they are, so all have been forbidden.

Rodents, reptiles, amphibians, and insects (except as mentioned above) are all forbidden. Lev. 11:29-30, 42-43. from jewfaq.org