Not only have I heard of the Noachidim/Noahides, I actively identified with/practiced this way of life for about a year. So maybe I can shine some light on the matter.
Firstly, the Noachide movement centers around the ‘Seven Laws of Noach’.
Conceptually speaking, these are somewhat similar to the Ten Commandments in that they serve as both broad categories of law (e.g. by encompassing many mitzvot/laws outside of the seven) and concise units of self-contained law in of themselves.
Though the link above goes into more detail on these, in short the laws exhort us not to worship (or ideally, even to mention) any deity but the One God; never to take parts from a living creature (for example, skinning animals for their fur while they’re still very much alive and conscious, God forbid); not to blaspheme the One God; not to cause undue harm or violence towards God’s Creation (this including licentious sexual relations, and thievery); and finally to establish courts of law to disseminate and enforce these laws among the gentiles that these laws apply to.
Elaborating on that last point a little bit, these seven laws do in fact only apply to the Gentiles according to the Torah worldview. Where the 613 ‘main’ mitzvot of the Torah (written and oral) apply to the Jews, these seven laws apply to the Gentiles.
In fact, these seven laws are not unique; they derive from the same pool as the laws for Jewry does. The main discerning factor is that these specific seven were decreed as binding on the Gentiles to both Adam and Noach.
(An interesting side-note is that there were originally only six laws revealed to Adam; the seventh, Eiver Min HaChai [or not taking a part from a living animal] wasn’t given until the time of Noah.)
All of this considered, Noachide-ism has never been considered to be a religion in of itself; just a series of laws incumbent on humanity as a whole, a measure of goodness or righteousness if you will.
Just as we expect the man on the street not to murder or pickpocket his fellow (whether either party be Catholic, Muslim, atheist, Sikh, or any other religious affiliation for that matter), God expects these seven laws out of his human Creation as a basic code for living.
Some have tried to make a cohesive religious movement out of the Noachide laws, but this is generally frowned upon as a man-made addition to the seven laws HaShem has already given to humanity. The more common and accepted route is simple propagation of these laws, occasionally mingled with attempts to reconcile Noachian law with pre-existing religion (see this page for an example of the latter).
Most of the laws are fairly self-explanatory, but the seventh (establishing courts of Noachian Law) is perhaps the most intriguing. Originally, these courts were in existence and regular operation up until the destruction of the Temple in Jerusalem. They enforced matters of morality and meted out capital punishments as the Oral Law dictates.
Actually, to the best of my knowledge, there was just one main court; and that was the Sanhedrin. Catholics might know this court better as the Pharisaical court which condemned the Christ to death for heresy.
After the coming of the Messiah, these courts will be re-established under his care and the full Noachian way of life will be restored replete with the fully-functioning legal system.
A good modern-day comparison to this is the legal system used by orthodox Jews (the beis din, or ‘house of law’). However, instead of serving the community on a shul-to-shul (or community-to-community) basis, this Sanhedrin would serve to judge Gentiles on a more universal level.
Overall, these laws are sourced from the oral tradition of Torah (the Mishnah, Shulchan Aruch, rulings of various rabbonim, and so on). The individual laws can be seen in the biblical texts, but the oral laws are what expound on them and make them more cohesive.
Some good sources of first-hand information on these laws are Ask Noah, WikiNoah, and the UK Noahide Blog.
If you’re interested in more in-depth coverage of the finer details of Noachian laws, Rabbi Moshe Weiner of the AskNoah organization has released a book called The Divine Code which covers them all pretty thoroughly. It’s a little chunky (almost 700 pages), but if you’re looking for information on the subject in English that’s a good place to start.
Hopefully that shed some light on the subject (and wasn’t too verbose or link-filled!). I have a tendency to repeat myself or go into too much detail on things sometimes, but so it goes. If an
Also, this is my first actual post on the board after months of lurking. So greetings! Looking forward to getting to know you guys as time goes on.