When God addressed Moshe there was an accompanying miracle (and there's midrash about Avraham's case being special too), so it was pretty clear what was happening, but how did the other prophets come to know that it was God who was speaking to them -- not a delusion, not a trick, but divine communication? Was it immediate, or could there have been some period during which the prophet wasn't yet sure what was happening to him?
(This question arose out of why did Yonah run away?.)
In general, it seems the prophet would fall into a prophetic state, so it would be clear that it wasn't just a random voice speaking to him. See, for example, Berishis 15 where God appears to Avraham first in "a vision", and then in "a deep sleep... a dread, a great darkness".
However, it seems that sometimes Nevuah sounded just like a person's voice, and the prophet could have initially confused it for a person speaking. See Shemuel 3 where Shemuel repeatedly mistakes the voice of God for Eli's. The passuk explains why this could happen:
Now Samuel did not yet know the LORD, neither was the word of the LORD yet revealed unto him
So it seems in certain cases there "could have been some period during which the prophet wasn't yet sure what was happening to him".
Rambam Hilchos Yesodei Hatorah chapter 7:1, 3 indicates that the person receiving the prophecy is a clear thinker whose mind is connected with God constantly. He states:
ובעת שתנוח עליו הרוח--תתערב נפשו במעלת המלאכים הנקראים אישים, וייהפך לאיש אחר, ויבין בדעתו שאינו כמות שהיה, אלא שנתעלה על מעלת שאר בני אדם החכמים
Therefore I believe that the prophet does know that she or he is having a true spiritual experience, though, based on the story with Samuel cited in the other answer I would wager to say it is unclear exactly the nature of that experience. Meaning, is it divine inspiration (ruach hakadosh), an angelic revelation, a bat-kol or actual prophecy.
See also, the Rambam's Guide for the Perplexed pt. III, chapters 32-48.
This question was asked to R. Joseph Messas in Otzar Hamichtavim Vol. III # 1,813.
שאל כבודו איך ידעו הנביאים שהקב"ה מדבר עמהם הלא כתיב לא יראני האדם וחי ואם לא רואים את המדבר איך יודעים מי מדבר
His Honor asked how the prophets knew that the Holy-One-Blessed-be-He was speaking to them. Is it not written, "no man can see Me and survive"? And if they did not see the speaker how did they know who was speaking?
R. Messas acknowledged that this was a serious question ("שאלה גדולה שאלת") and first referred the questioner to earlier sources that discuss this topic. Then he tried to answer the question himself. Essentially, he answered that even though God has no physical form, the prophet would always see some sort of image (which would vary for different prophecies) and could sense God's voice emanating from the image.
This question was also addressed by R. Saadia Gaon in Emunot V’Deiot 3:5
I also considered the question of how the prophet could be sure that the message that he heard came from God before ascribing it to his Lord in the presence of his people, and I arrived at the conclusion that this was effected by means of some sign that would appear to him at the beginning of the colloquy and remain until its termination. This sign could take the form of a pillar of fire or a pillar of cloud or a light that did not emanate from the ordinary luminaries. When, then, the prophet saw such a sign, he was certain that the message came from God.
(Rosenblatt translation)
