Okay, I've decided to cheat a little.
by Nehemia Gordon. The outline can be found here:
1. No domesticated animals (bull, goat, sheep) may be slaughtered except as a sacrifice. The sacrificial flesh may be eaten but only in a state of ritual purity. The blood must be poured out on the altar. (Lev 17:3-12)
2. Wild animals (e.g. deer, gazelle) and birds may be killed anywhere and eaten as non-sacrifice while in a state of ritual impurity. The blood must be spilled on the ground and covered with earth. (Lev 17:13-14)
3. When you are far from the chosen place (Tabernacle, Temple) you may slaughter domesticated animals as non-sacrifices. The blood must be spilled "on the ground like water", i.e. not on an altar outside the Temple. (Dt 12:13-27)
4. Sacrifices must still be brought to the Temple, even if you are far away and the blood spilled on the altar. (Dt 12:13-27)
The 2 Torah chapters in question:
Tanach - Leviticus Chapter 17
1. And the Lord spoke to Moses, saying,
2. Speak to Aaron, and to his sons, and to all the people of Israel, and say to them; This is the thing which the Lord has commanded, saying,
3. Which ever man there is of the house of Israel, who kills an ox, or lamb, or goat, in the camp, or who kills it out of the camp,
4. And brings it not to the door of the Tent of Meeting, to offer an offering to the Lord before the tabernacle of the Lord; blood shall be imputed to that man; he has shed blood; and that man shall be cut off from among his people;
5. To the end that the people of Israel may bring their sacrifices, which they offer in the open field, that they may bring them to the Lord, to the door of the Tent of Meeting, to the priest, and offer them for peace offerings to the Lord.
6. And the priest shall sprinkle the blood upon the altar of the Lord at the door of the Tent of Meeting, and burn the fat for a sweet savor to the Lord.
7. And they shall no more offer their sacrifices to demons, after whom they play the harlot. This shall be a statute forever to them throughout their generations.
8. And you shall say to them, Whoever there is of the house of Israel, or of the strangers who sojourn among you, who offers a burnt offering or sacrifice,
9. And brings it not to the door of the Tent of Meeting, to offer it to the Lord; that man shall be cut off from among his people.
10. And whoever there is of the house of Israel, or of the strangers who sojourn among you, who eats any kind of blood; I will set my face against that soul who eats blood, and will cut him off from among his people.
11. For the life of the flesh is in the blood; and I have given it to you upon the altar to make an atonement for your souls; for it is the blood that makes an atonement for the soul.
12. Therefore I said to the people of Israel, No soul of you shall eat blood, nor shall any stranger who sojourns among you eat blood.
13. And whoever there is of the people of Israel, or of the strangers who sojourn among you, who hunts and catches any beast or bird that may be eaten; he shall pour out its blood, and cover it with dust.
14. For it is the life of all flesh; the blood of it is for its life; therefore I said to the people of Israel, You shall not eat the blood of any kind of flesh; for the life of all flesh is its blood; whoever eats it shall be cut off.
15. And every soul who eats that which died of itself, or that which was torn by beasts, whether he is one of your own country, or a stranger, he shall both wash his clothes, and bathe himself in water, and be unclean until the evening; then shall he be clean.
16. But if he washes them not, nor bathe his flesh; then he shall bear his iniquity.
Tanach - Deuteronomy Chapter 12
1. These are the statutes and judgments, which you shall take care to do, in the land, which the Lord God of your fathers gives you to possess all the days that you live upon the earth.
2. You shall completely destroy all the places, where the nations which you shall possess served their gods, upon the high mountains, and upon the hills, and under every green tree;
3. And you shall overthrow their altars, and break their pillars, and burn their Asherim with fire; and you shall cut down the carved images of their gods, and destroy their names out of that place.
4. You shall not do so to the Lord your God.
5. But to the place which the Lord your God shall choose out of all your tribes to put his name there, to his habitation shall you seek, and there you shall come;
6. And there you shall bring your burnt offerings, and your sacrifices, and your tithes, and offerings of your hand, and your vows, and your freewill offerings, and the firstlings of your herds and of your flocks;
7. And there you shall eat before the Lord your God, and you shall rejoice in all that you put your hand to, you and your households, because the Lord your God has blessed you.
8. You shall not do after all the things that we do here this day, every man whatever is right in his own eyes.
9. For you are not as yet come to the rest and to the inheritance, which the Lord your God gives you.
10. But when you go over the Jordan, and live in the land which the Lord your God gives you to inherit, and when he gives you rest from all your enemies around, so that you live in safety;
11. Then there shall be a place which the Lord your God shall choose to cause his name to dwell there; there shall you bring all that I command you; your burnt offerings, and your sacrifices, your tithes, and the offering of your hand, and all your choice vows which you vow to the Lord;
12. And you shall rejoice before the Lord your God, you, and your sons, and your daughters, and your menservants, and your maidservants, and the Levite who is inside your gates, for he has no part nor inheritance with you.
13. Take heed to yourself that you offer not your burnt offerings in every place that you see;
14. But only in the place which the Lord shall choose in one of your tribes, there you shall offer your burnt offerings, and there you shall do all that I command you.
15. However you may slaughter animals and eat their meat in all your gates, to your hearts desire, according to the blessing of the Lord, your God which he has given you; the unclean and the clean may eat of it, as they do of the gazelle and the deer.
16. Only you shall not eat the blood; you shall pour it upon the earth like water.
17. You may not eat inside your gates the tithe of your grain, or of your wine, or of your oil, or the firstlings of your herds or of your flock, nor any of your vows which you vow, nor your freewill offerings, or offering of your hand;
18. But you must eat them before the Lord your God in the place which the Lord your God shall choose, you, and your son, and your daughter, and your manservant, and your maidservant, and the Levite who is inside your gates; and you shall rejoice before the Lord your God in all that you put your hands to.
19. Take heed to yourself that you forsake not the Levite as long as you live upon the earth.
20. When the Lord your God shall enlarge your border, as he has promised you, and you shall say, I will eat meat, because your soul longs to eat meat; you may eat meat, to your hearts desire.
21. If the place which the Lord your God has chosen to put his name there is too far from you, then you shall kill of your herd and of your flock, which the Lord has given you, as I have commanded you, and you shall eat in your gates, to your hearts desire.
22. Like the gazelle and the deer are eaten, so you shall eat them; the unclean and the clean shall eat of them alike.
23. Only be sure that you eat not the blood; for the blood is the life; and you may not eat the life with the flesh.
24. You shall not eat it; you shall pour it upon the earth as water.
25. You shall not eat it; that it may go well with you, and with your children after you, when you shall do that which is right in the sight of the Lord.
26. Only your holy things which you have, and your vows, you shall take, and go to the place which the Lord shall choose.
27. And you shall offer your burnt offerings, the meat and the blood, upon the altar of the Lord your God; and the blood of your sacrifices shall be poured out upon the altar of the Lord your God, and you shall eat the meat.
28. Observe and hear all these words which I command you, that it may go well with you, and with your children after you forever, when you do that which is good and right in the sight of the Lord your God.
29. When the Lord your God shall cut off the nations from before you, where you go to dispossess them, and live in their land;
30. Take heed to yourself that you be not snared by following them, after they are destroyed from before you; and that you inquire not about their gods, saying, How did these nations serve their gods? that I may also do likewise.
31. You shall not do so to the Lord your God; for every abomination to the Lord, which he hates, have they done to their gods; for even their sons and their daughters they have burned in the fire to their gods.
Basically, the Torah provides locations for slaughters, and states that the blood is either to be spilled on the ground and covered, or spilled on the altar. I would consider that as defining a method of slaughter
. However, If you're looking for the particulars of where and how to cut, the you do need the Talmud.
As an aside, I'd point out that even those who claim to only eat kosher by Biblical standards need to stay away from the meat found in most supermarkets. In the case of cattle, they are killed with a blow to the head, and the blood is allowed to stay in the body long enough to congeal, thus making the meat unkosher by both Talmudic as well as Biblical definitions.