A Noachide is a ben-Noach, or son of Noah. This means any human being who is descended from Noah.
Since Noah and his family were the only humans to survive the flood, every human being alive today is a Noachide by birthright.
This is the plain and simple meaning of ben-Noach, but depending on your beliefs it can have suprising implications. To declare yourself a Noachide in contrast to being a Christian, Muslim or Buddhist often has a slightly different meaning to it (although in the end the meaning is really the same).
You see, a Noachide is not a Jew. A Noachide is also not a Christian, a Muslim, or anything else. A Noachide is a son of Noah – a ben-Noach. That's it.
This is important because God made a covenant with Noach (Noah) that stands to this day – nowhere in the bible is it shown to have ended. This is similar to God's commandments to Adam; when God said to Adam, “Be fruitful and multiply,” (Genesis 1:28), this would also apply to Noah and his descendants. In fact, this is specifically mentioned as a commandment to Noah in Genesis 9:7.
However then, is there a difference between ben-Adam and ben-Noach? Yes. In Genesis 1, Adam is instructed that every fruit (bearing seed) will be for him as food; but in Genesis 9 Noah is also told that every moving thing that lives may be eaten for food. The commandment goes on then to specify that one shall not eat (or drink) blood, and not to eat any part of a living animal.
The commandments may be written in various ways, also their number may vary depending on the specifics of their wording. For example, in Genesis 2:24 God stated that a man would leave his mother and father and cleave to his wife. This is a commandment in as much as it is a statement by God, therefore it is used to state “Do not have forbidden sexual relationships”. All in all the commandments given, by God, to Noah and his descendants (Genesis 9:9) are as follows:
Genesis 2:16 states: “And L-rd G-d commanded to the man, saying…” This Divine command to Adam implies that only the One True G-d, the Creator of the spiritual and physical realms, should be obeyed and honored as the Deity, and the greatest honor is to serve and worship Him. Thus, one should serve and worship only the One True G-d, and not any idol. 
Leviticus 24:10-17 relates the incident of a Jew who violated the injunction of Exodus 22:27 and blasphemed in anger. Moreover, Leviticus 24:15 in Hebrew states: “ish ish” (“any man”) who curses his G-d shall bear his sin.” Why the double expression of “ish ish” (literally: “a man, a man”)? To include all mankind, Jews and Gentiles. This demonstrates that blasphemy thus is prohibited to Gentiles even as it is for Jews. 
The edict against murder, and the punishment for this transgression, is stated in Genesis 9:5-6: “…of man for his brother, I [G-d] will demand the soul of man. Whoever sheds the blood of man, among man, his blood shall be shed; for in the image of G-d He made man.”
Five of the six types of relations that are forbidden by G-d to Gentiles are covered in Genesis 2:24: “Therefore a man shall leave his father and his mother and cling to his wife, and they shall become one flesh.” This verse explicitly forbids relations with one’s mother, with a woman who has ever been his father’s domestic partner or certified wife, with a woman who is currently a domestic partner or certified wife of another man, with another male, or with an animal. A Gentile is also forbidden to have relations with his maternal sister, which is learned from Gen. 20:13: “Moreover, she is indeed my sister, my father’s daughter, though not my mother’s daughter; and she became my wife.” (Note that Abraham said this to appease Abimelech. It was actually only figuratively true in his case, since Sarah was the daughter of Abraham’s brother. So they had the same paternal grandfather, who people often referred to as “father.”)
It also was universally accepted that father-daughter relations would be included, as evidenced by the disgrace of Lot after he had relations with his two daughters, following G-d’s destruction of Sodom and Gomorrah (Gen. 19:29-36, and Rashi’s explanation of Gen. 20:1). Relations of a female with a female are likewise an abomination to G-d which is included as one of the subjects of the verse Lev. 18:3, which speaks against the immoral practices of the ancient Egyptians and Canaanites, and which Lev.18:30 refers to as “abominable traditions.” About these, the Midrash (Sifra) specifies: “A man would marry a man, a woman would marry a woman, and a woman would be married to two men.”
The prohibition of theft is contained within the permission which G-d granted to Adam and Hava (Eve) in Genesis 2:16 to eat from the trees of the garden. This implies that if the permission had not been granted, they would have been forbidden to do so, because the property did not belong to them. This applied specifically to the fruit of the Tree of “Knowledge of Good and Evil” which was forbidden for them to take, under penalty of death (Genesis 2:17). This commandment was cited explicitly by Abraham in Genesis 21:25.
Adam and Hava (Eve) were not given permission to kill animals for food, and this remained in effect until after the Flood. G-d permitted the eating of meat for the first time to Noah and his family after they left the Ark, which is why G-d at that time added the seventh commandment, which prohibits the eating of meat that was severed from a living animal (even if it was stunned and insensitive). This commandment given to Noah is recorded in Genesis 9:4: “But meat, with its soul [which is in] its blood you shall not eat.”
G-d commanded Noah regarding the trial and punishment of a murderer, as it says in Genesis 9:6, “Whoever sheds the blood of man, among man, his blood shall be shed…” This refers to a Noahide commandment to judge and penalize a murderer. This is explained as follows by the Talmudic Sages: “Whoever sheds the blood of man” (referring to the murderer), “among man” (i.e., he is to be prosecuted in a court by a man who is qualified to testify as a witness), “his blood shall be shed” (if convicted, he is liable to capital punishment by the court). The Noahide Code specifies that Gentile societies are obligated to abide by justice through establishing a system of righteous courts of law.
1. We recognize that all human beings are sons of Noah and are therefore bound by these laws. 2. We recognize that these laws are still binding (to us and to everyone!) as instituted by God in his promise and the sign of the Rainbow.
No other covenant has removed the validity of these laws, God's covenant with the Earth. The Jewish laws generally include these laws in one form or another, and most Christians or Muslims would also find it unacceptable to violate these laws.