(1) Miriam and Aaron spoke against Moses because of the Cushite woman he had taken [into his household as his wife]: “He took a Cushite woman!” (2) They said, “Has ה' spoken only through Moses? Has [God] not spoken through us as well?” And ה' heard it.

(3) Now Moses himself was very humble, more so than any other human being on earth. (4) Suddenly ה' called to Moses, Aaron, and Miriam, “Come out, you three, to the Tent of Meeting.” So the three of them went out. (5) ה' came down in a pillar of cloud, stopped at the entrance of the Tent, and called out, “Aaron and Miriam!” The two of them came forward;

(6) and [God] said, “Hear these My words: When prophets of ה' arise among you, I make Myself known to them in a vision, I speak with them in a dream. (7) Not so with My servant Moses; he is trusted throughout My household. (8) With him I speak mouth to mouth, plainly and not in riddles, and he beholds the likeness of ה'. How then did you not shrink from speaking against My servant Moses!”

(9) Still incensed with them, ה' departed.

(10) As the cloud withdrew from the Tent, there was Miriam stricken with snow-white scales! When Aaron turned toward Miriam, he saw that she was stricken with scales.

(11) And Aaron said to Moses, “O my lord, account not to us the sin which we committed in our folly. (12) Let her not be like a stillbirth which emerges from its mother’s womb with half its flesh eaten away!” (13) So Moses cried out to ה', saying, “O God, pray heal her!”

(14) But ה' said to Moses, “If her father spat in her face, would she not bear her shame for seven days? Let her be shut out of camp for seven days, and then let her be readmitted.” (15) So Miriam was shut out of camp seven days; and the people did not march on until Miriam was readmitted.

And whence did Miriam know that Moses had separated himself from his wife (for this was the statement she made; cf. Rashi below)? R. Nathan answered: “Miriam was beside Zipporah When it was told to Moses, ‘Eldad and Medad are prophesying in the camp’ (Numbers 11:27). When Zipporah heard this, she exclaimed, Woe to the wives of these if they have anything to do with prophecy, for they will separate from their wives just has my husband has separated from me!”

It was from this that Miriam knew about it, and she told it to Aaron. Now what was the case with Miriam who had no intention to disparage him? She was punished thus severely! How much the more will this be so in the case of one who intentionally speaks in disparagement of this fellow”! (Sifrei Bamidbar 99).

How did Miriam know that Moses had separated from his wife Tzipporah?

Seeing that Tzipporah did not adorn herself as other (married) women did, she asked her for the cause and was told: "Your brother is not 'particular' about this thing." Thus Miriam learned of the matter. She apprised Aaron of it and they both spoke of it.

Now does this not follow a fortiori, viz.: If Miriam, whose intent was not to berate her brother, but to praise him, and not to diminish propagation (in Israel), but to increase it, and who spoke thus privately — If she was thus punished, then one who intends to speak against his brother, in defamation and not in praise, and to diminish propagation and not to increase it, and in public — how much more so (is he to be punished!)
...There are those who are beautiful in appearance, but not in deed; in deed, but not in appearance, viz. (Proverbs 11:22) "Like a golden ring in the snout of a pig is a beautiful woman lacking in sense."

Tzipporah was beautiful in both — wherefore it is written "about the Cushite woman that he had taken, for he had taken a Cushite woman."

(25) Then, after coming down in a cloud and speaking to him, ה' drew upon the spirit that was on him and put it upon the seventy participating elders. And when the spirit rested upon them, they spoke in ecstasy, but did not continue. (26) Two of the participants, one named Eldad and the other Medad, had remained in camp; yet the spirit rested upon them—they were among those recorded, but they had not gone out to the Tent—and they spoke in ecstasy in the camp. (27) An assistant ran out and told Moses, saying, “Eldad and Medad are acting the prophet in the camp!” (28) And Joshua son of Nun, Moses’ attendant from his youth, spoke up and said, “My lord Moses, restrain them!” (29) But Moses said to him, “Are you wrought up on my account? Would that all Hashem's people were prophets, that ה' put [the divine] spirit upon them!”

It is [one] of the foundations of [our] faith that God conveys prophecy to man.
Prophecy is bestowed only upon a very wise sage of a strong character, who is never overcome by his natural inclinations in any regard. Instead, with his mind, he overcomes his natural inclinations at all times. He must [also] possess a very broad and accurate mental capacity.
A person who is full of all these qualities and is physically sound [is fit for prophecy]. When he enters the Pardes and is drawn into these great and sublime concepts, if he possesses an accurate mental capacity to comprehend and grasp [them], he will become holy. He will advance and separate himself from the masses who proceed in the darkness of the time. He must continue and diligently train himself not to have any thoughts whatsoever about fruitless things or the vanities and intrigues of the times.
Instead, his mind should constantly be directed upward, bound beneath [God's] throne [of Glory, striving] to comprehend the holy and pure forms and gazing at the wisdom of the Holy One, blessed be He, in its entirety, [in its manifold manifestations] from the most elevated [spiritual] form until the navel of the earth, appreciating His greatness from them. [After these preparations,] the divine spirit will immediately rest upon him.
When the spirit rests upon him, his soul becomes intermingled with the angels called ishim, and he will be transformed into a different person and will understand with a knowledge different from what it was previously. He will rise above the level of other wise men, as [the prophet, Samuel] told Saul [I Samuel 10:6]: "[The spirit of God will descend upon you] and you shall prophesy with them. And you will be transformed into a different person."