The prohibition of idolatry is the first Noachide law[1] and is one of the two that only apply to gentiles who accept Hashem.
Gentiles are forbidden from serving or believing in the divinity of any false gods or entities besides Hashem, provided they are aware of Hashem. Je-SUS and other non-divine characters who are claimed to be a part of Hashem are permitted, though not encouraged, for gentiles. Believing that Ze-us is the god of lightning is forbidden (if the believer knows Hashem), because that would be a power outside of Hashem. Believing that Ze-us is a creation of Hashem and is subservient to him is, while incorrect, permissible. Believing in magic, even if it is believed to be from Hashem, is forbidden, along with belief in astrology determining events, omens, quantum or crystal healing, quantum mysticism, luck, the Devil, spirit channeling, and other similar things.
Gentiles are also forbidden from creating, purchasing, or owning idols, which are images of false gods, though some idolatry (such as quantum mysticism) has no physical representation A gentile is allowed to keep his idols, by annuling them[2], thereby causing them to no longer be idols. The following is the list of things one can do to annul an idol and is an entirely comprehensive list[3]: cutting off the tip of its nose, ear, or finger, defacing it, damaging it, distorting its face, or abandoning it in a time of peace (when no war is ongoing).
This law also contains a positive obligation to accept Hashem (once sufficient evidence for him has been provided), and the obligation to pray at least in times of need.