If the laws of Noah are the laws for the nations and they are handed down by Jewish oral tradition, how are the nations to know them?
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In short: Jews.
The 7 Laws of Noah are encoded in the Torah, and were given to all of mankind even before the rest of the Torah was revealed. (By "encoded" I mean that they aren't incredibly obvious from the text itself; rather, the sages explained the verse in the Talmud.) Most of the 7 laws are obvious rules of morality (prohibitions against stealing, killing, etc.,).
Where possible, Jews are commanded to be a "light unto the nations", i.e., to let the world know about these commandments. For much of history (especially recent history) Jews have not been in a position to do this publicly, due to the fact that they were being oppressed, and trying to teach your oppressor morality doesn't work too well in real life.
However, nowadays, when it is possible in most of the world to spread these teachings without harm, there has been a revival of "Noahidism". The Lubavitcher Rebbe, for one, was very public in saying that Jews now have an obligation to spread the knowledge of these laws, and many of his Shluchim and followers are active in this.
From Noahide.org adapting the words of the Lubavitcher Rebbe:
As far as where one can learn about these laws, the aforelinked site Noahide.org has articles and links to other resources.
A Noahide friend of mine is a big fan of Rabbi Moshe Weiner's book The Divine Code, which clearly delineates what Jewish Tradition understands the 7 Noahide Laws require.