Sanhedrin, Chapter 11, Mishnah 5. We have reached the fourth of the six transgressions for which the punishment is strangulation - the false prophet. This transgression can occur in one of two ways, as the Mishnah will detail explicitly, and both are derived from the verse.
The source of the law in the verse:
In the Book of Devarim (Chapter 18, verse 20) it is stated: "But the prophet who intentionally speaks a word in My Name, which I did not command him to speak". This verse includes two cases:
"Who intentionally speaks a word in My Name" - one who says something that he never heard from Hashem at all, yet he transmits it in the Name of Hashem as if it were said to him.
"Which I did not command him to speak" - even if Hashem indeed said the words, but He said them to Prophet A, and Prophet A transmitted them to his friend, and his friend went and said them in the Name of Hashem. That person is not a prophet, but is merely repeating what he heard from the prophet.
These two cases are essentially false prophecy - whether because Hashem did not say the words at all, or because He did not say them to this person - and therefore the punishment for them is strangulation.
The wording of the Mishnah - what is punishable by death at the hands of man:
The Mishnah lists two cases: "Hemitnabeh mah shelo shama" - one who prophesies about something he did not hear from Hashem, "umah shelo ne'emar lo" - something that Hashem indeed said, but He did not command him to transmit it. For these two transgressions "mitaso bidei adam" - his death is at the hands of man, meaning strangulation in court - provided there were witnesses and a warning.
What is punishable by death at the hands of Heaven:
In contrast, the Mishnah lists cases involving disobedience to a prophecy, for which the death penalty is at the hands of Heaven:
"Hakoveish es nevuaso" - a prophet who does not transmit what he was commanded to transmit. For example, in the story of Yonah the prophet: Hashem told him "go to Nineveh", and for various reasons he did not want to fulfill this, and he suppressed his prophecy by not transmitting the word of Hashem. This act is invalid, but it is not the crime of a false prophet.
"Hamevater al divrei navi" - one who disregards the words of a prophet, meaning he ignores them or treats them lightly, not taking them seriously and not fulfilling them properly. This too is a transgression, but not the transgression of a false prophet whose punishment is death by the court.
"Venavi she'avar al divrei atzmo" - and a prophet who transgresses his own words, meaning a prophet who disobeys a command that he was explicitly commanded. The Gemara brings the example of Ido the prophet, who was commanded to go to Yarovam ben Nevat and not to eat or drink until his return home. On his way back, he met another prophet, who told him that Hashem had commanded him to dine with him, and he went with him and ate and drank before returning home - and by doing so, he transgressed what Hashem explicitly commanded him not to do.
For transgressions of this type "mitaso bidei Shamayim" - his death is at the hands of Heaven. These too are severe transgressions that carry a death penalty, but it is only at the hands of Heaven: this is not a death penalty in court, but rather the person loses his right to live due to this transgression, and therefore a premature death will be decreed upon him if he does not repent.
As it is stated: "And the man who will not hearken to My words which he shall speak in My Name, I will require it of him" - the man who does not listen to the words of Hashem spoken in His Name by the prophet, Hashem Himself, so to speak, will hold him accountable. From here we see that the death is at the hands of Heaven and not at the hands of man.
In summary: In this Mishnah we learned that a false prophet - one who prophesies what he did not hear or what was not said to him - is put to death by a human court through strangulation; whereas one who suppresses his prophecy, one who disregards the words of a prophet, and a prophet who violates his own words - their death is at the hands of Heaven, as is derived from the verse, "I will require it of him."