The prohibition of cursing Hashem (chas veshalom) is the second noachide law.
It is forbidden to curse any word which refers to Hashem, and especially one of the seven primary Hebrew names, most importantly the one which the word 'Hashem' refers to. This includes the prohibition of saying words for Hashem in undignified situations, such as in a room in which someone is naked.
It is forbidden to say such words near filth or in a filthy room, such as feces and a bathroom respectively. This may be the only situation in which saying Shalom is forbidden.
It is forbidden to say such as word for no reason or for a vain reason. If one does, they should immediately bless the name (e.g. 'blessed be he forever')
Depending on one's rav, if one makes a vow on Hashem, they are obligated to fulfill it.
It is forbidden to curse someone (e.g. "may H-shem curse you"), or at least a judge or a Jew. [If one 'curses' someone using magic or similar means, it is violating a different noachide law, the prohibition of idolatry.]
It is forbidden for a gentile to ever (at least in olam hazeh), under any circumstances, besides being told to do so or else someone will be killed, pronounce (or attempt to) the yud-kei-vav-kei name of Hashem.
It is forbidden to destroy a text that contains a Hebrew name of Hashem.
It is forbidden to create material which obfuscates or denies the fact that the Torah is divine or that Hashem 'exists' (such as an atheist video claiming that the Torah was not from Hashem).
It is non-ideal to throw away or destroy a text that contains a non-Hebrew name of Hashem, unless it promotes or proselytizes idolatry.
It is an obligation to generally respect Hashem's names.
It is an obligation to fear Hashem.
It is an obligation to seek out evidence for Hashem 'existing' or the Torah being divine if one is an atheist. The world was created so we can serve Hashem, so someone who prioritizes relatively vain subjects over becoming sure that Hashem 'exists' or that the Torah is divine is wasting their time.