From the Mishneh Torah – Melachim uMilchamot – Chapter 9:14
A gentile who transgresses these seven commands shall be executed by decapitation. For this reason, all the inhabitants of Shechem were obligated to die. Shechem kidnapped. They observed and were aware of his deeds, but did not judge him.
A gentile is executed on the basis of the testimony of one witness and the verdict of a single judge. No warning is required. Relatives may serve as witnesses. However, a woman may not serve as a witness or a judge for them.
From the Mishneh Torah – Melachim uMilchamot – Chapter 9:2
A gentile who worships false gods is liable provided he worships them in an accepted manner.
A gentile is executed for every type of foreign worship which a Jewish court would consider worthy of capital punishment. However, a gentile is not executed for a type of foreign worship which a Jewish court would not deem worthy of capital punishment. Nevertheless, even though a gentile will not be executed for these forms of worship, he is forbidden to engage in all of them.
From the Mishneh Torah – Melachim uMilchamot – Chapter 10:5-6
A gentile who converts after cursing God’s name, worshipping false gods, engaging in relations with a colleague’s wife, or killing a fellow gentile is exempt from punishment.
In contrast, if he converted after killing a Jew or having relations with a Jew’s wife, he is liable. He is decapitated for killing the Jew and strangled to death for engaging in relations with a Jew’s wife. He is given the latter punishment because the laws governing him have changed.
It has already been explained that gentiles are always executed by decapitation except in cases when one engages in relations with the wife of a Jew or a consecrated maiden. In the latter instance, he is stoned to death.
If he engaged in relations with a Jew’s wife after they married, but before they ever engaged in relations, he is executed by strangulation.
The Talmud lists the punishment for blaspheming the Ineffable Name of God as death. The sons of Noah are to be executed by decapitation for most crimes, considered one of the lightest capital punishments, by stoning if he has intercourse with a Jewish betrothed woman, or by strangulation if the Jewish woman has completed the marriage ceremonies, but had not yet consummated the marriage.
From the Talmud – Sanhedrin 57a:13
Rav Huna, Rav Yehuda, and all of the other students of Rav say: A descendant of Noah is executed for transgressing any of the seven Noahide mitzvot; the Merciful One revealed this punishment with regard to one mitzva, the prohibition of bloodshed, and the same is true with regard to all of them.
Prospectives on Noahide Laws Chapter 5:
The Noahide laws are generally held to be so evident and normal that one cannot plead ignorance or lack of warning to be exempt from liability for their non-observance. The theoretical punishment of the Torah for transgression of the Noahide laws is death, although such a penalty could only be enforced at a time when the great Sanhedrin, the Jewish High Court, convened in its place on the Temple Mount, and it seems that even when that was the case, this penalty was almost never carried out.
The significance of the theoretical death penalty in general, whether for Jew or non-Jew, is given in the words of Rashi, namely that “one has transgressed the will of one’s Creator”. In the case of the Noahide laws, it is that the very purpose for which a human was created, namely to settle the world peacefully has been contradicted and, and so also the essential point of the human being’s existence has been vitiated.