Qitzur Shulchan Arukh – 67:8
How do we unbind/permit the neder or shevu’ah? He goes to three men who are committed to the Torah, where one of them is adept in the laws of nedarim so that he will know which nedarim can be unbound and which of them can not be unbound, and how they are unbound, and these [three] permit it for him.
And someone who makes a neder in a dream, it is better that 10 who are committed to the Torah permit it for him.
This being the Qitzur, we aren’t really told how one is released from an oath. Rather, he is told to go to the beis din and they’ll know what to do. The key to hataras nedarim is showing how the neder was based on incorrect or incomplete information, and was therefore made in error. I assume that’s vague enough to avoid abuse by someone who only thinks they know what they’re doing, and thus in the spirit of our text.
The second piece isn’t halakhah, as can be seen in the “tov she- — it is better that” rather than a requirement. A neder made in a dream could be seen as less binding, since there was no thought reinforced by speech. On the other hand, it shows something going on at a deeper level of the person’s persona. Therefore it doesn’t really require annulment from a halachic standpoint, but the person may wish to work out what’s going on — and thus the value of a minyan.