In response to a frequently asked question about where in the Torah
we can find the Seven Noahide Laws, I have prepared this short list,
it is by no means exhaustive.

The Seven Noahide Laws are found in the book of Genesis, but they are
found in their transgression, not as specific commandments. In other words
when one of these laws was transgressed, comment is made in Genesis that
these were sins.

All references are from the Jewish text.

1. Idolatry Gen. 31:19-36 Rachel stole the images (idols) of her brother Laban.

Gen. 31:19 Laban had gone to shear his sheep, and Rachel stole the
teraphim¹ that belonged to her father.

1. v. 19. And Rachel stole the teraphim that belonged to her father. The Teraphim were idols, and
Rachel took them to keep Laban from idol worship (Rashi). The Torah records this episode because
her intentions were noble. (Midrash) Ramban derives the word from the root rapha, weak
[see Exodus 5.17], alluding to the "weakness" of their prognostications. The Zohar relates the
word to 'trph' and 'tvrph', denoting obscenity. Many consider them to have been household gods,
supposed to be the protectors of the home, similar to the later Roman Penates, which were
consulted as oracle {R' Hirsch).

2. Blasphemy Gen. 3:1-4 The Serpent falsely accused G-d.

Gen. 3:1-4 Now the Serpent was cunning beyond an beast of the field that
HaShem G-d had made. He said to the woman, "Did, perhaps, G-d say:
"You shall not eat of any tree of the garden?"

The Serpent lied, and misrepresented what G-d really said. The serpent was false attributing to
G-d that He had denied man access to 'any tree', when in fact only 'one' tree was forbidden.
In fact man was permitted to eat of every tree except one.

Gen. 2:16 And HaShem commanded man saying, "Of every tree of the
garden you may freely eat: 17 but the Tree of Knowledge of Good
and Bad, you must not eat thereof; for on the day you eat of it, you shall
surely die."

From Path of the Righteous Gentile by Clorfene and Rogalsky.

.     "The prohibition against blasphemy comes to teach us not to
       speak evilly against G-d, nor to detract from His exaltedness
       in any way by intentionally using words to lessen the reverence
       and faith befitting Him."

3. Murder Gen. 4.8-10-16, Gen. 6. Gen. 9:6. 4. Theft Gen. 2:17 Gen. 3.

Gen. 4:8 Cain spoke with his brother Abel, And it happened when they were in
the field, that Cain rose up against his brother Abel and killed him.

One of the reasons that the flood was sent was because of theft, violence, murder and
idolatry was common to all mankind. Gen. 6:11-12. The Commentary in the Stone
Edition Chumash says"

"Such is the progression of sin. It begins in private, when people still have
a sense of right and wrong. But once people develop the habbit of sinning,
they gradually lose their shame, and immoral behaviour becomes the
accepted - even required - norm. In Noah's time, the immoral sexual
conduct of the people extended to animals, as well, until they too
cohabited with other species."
Gen. 9:5-6 but of man, of every man for that of his brother I will demand the
soul of man. 6 Whoever sheds the blood of man, by man shall his blood be shed;
for in the image of G-d He made man.

4. Theft See Gen. 3:6, Gen. 31:19

Gen. 3:6 And the woman perceived that the tree was good for eating
and that it was a delight to the eyes, and that the tree was desirable
as a means to wisdom, and she took of its fruit and ate;

This was in direct disobedience of the command of G-d to not eat the fruit of that
particular tree.

Gen. 2:16 And HaShem commanded man saying, "Of every tree of the
garden you may freely eat: 17 but the Tree of Knowledge of Good
and Bad, you must not eat thereof; for on the day you eat of it, you shall
surely die."
Gen. 31:19 Laban had gone to shear his sheep, and Rachel stole the
teraphim¹ that belonged to her father.

5. Forbidden Sexual relationships Gen. 20.3 Abimelech knew adultery was a sin.
homosexuality Gen. 19:5-7.

Gen 20:3 And G-d came to abimilech in a dream by night and said to him,
"Behold you are to die because of the woman you have taken; moreover
she is a married woman."
Gen. 19:5-6 And they called to Lot and said to him, "Where are the men who
came to you tonight? Bring them out to us that we may 'know' them. 6 Lot
went out to them to the entrance, and shut the door behind him. 7 And he
said, "I beg you, my brothers, do not act wickedly.

The context clearly shows that the men of Sodom wished to have sexual relations with the
two men (angels), and Lot indicated that he knew that because he then showed how Sodom had
rubbed off on him, by offering the men his own virgin daughters.

6. Eating the Limb of a Living Animal Gen. 9.4-5.

Gen. 9:4-5 4 But flesh; with its soul its blood you shall not eat.
5 However, your blood which belongs to your souls I will demand, of
every beast will I demand it;

7. Establishing Courts of Justice Gen. 19:1-9. (The Gates of a city were where Judges
sat to convene Courts of Justice.) Ruth 4.1-11.

Gen. 19:1 The Two angels came to Sodom in the evening and Lot was
sitting at the gate of Sodom. ...... 9 And they said, "Stand back!"
Then they said, "This fellow came to sojourn and would act as a
Judge? Now we will treat you worse than them!"

For the origin of the Noahide Laws according to the Talmud check out this link.

http://www.oocities.org/rachav/oadnl.html