The method of enquiry depicted in Plato's dialogues is the dialectic - which bears some relationship to a procedure of question and answer - and this was taken up much later as a key term by Hegel then Marx; but I have never been able to understand what dialectic meant.
I read definitions, but they mean nothing to me - and in particular I could not understand why this method (and not another) was supposed to have a special kind of validity.
But it now strikes me that what is going on in Platonic dialogues should be considered in the light of what Socrates reported of his own motivation to do philosophy - in other words, the 'dialectic method' is simply the way of testing the knowledge of another person; to see whether he really understands the matter in hand.
In the Apology, Socrates describes his motivation as trying to find a man wiser than himself - to try and refute the Oracle at Delphi who stated there was nobody wiser than Socrates. So Socrates met and conversed-with various candidates for greater wisdom.
But how do you discover whether somebody is really wise, when they may be faking it, or they may believe that they understand - but really do not?
The only answer is that you need to 'apprentice' yourself to them - try to learn understanding from them to the extent that you can do it yourself.
Memorizing facts and relationships is not understanding. What is needed is to try and learn from the inside - so that having genuine understanding, new knowledge can be generated from that understanding.
It is a matter of understanding generating the answers; rather than a set of answers masquerading as understanding,
To know if an actual person himself understands, involves engaging him in a face-to-face, real time engagement - in a situation when whatever you get from that man comes from his mind (and not from a book).
The dialogue must be an open field, in which any topic can be addressed and probed to any depth.
This means that the would-be Master cannot simply prepare a set of answers in advance, but must respond to whatever subject at whatever length the questioner deems necessary; and must do this here and now.
Only if the Master knows the subject from the inside can he do this.
I take it that Euthyphro represents a (more or less) 'transcription' of the kind of thing Socrates did (since that seems to be the way this dialogue is presented, and indeed is its only justification since the dialogue doesn't really go anywhere).
And Euthyphro seems to correspond closely to what I have described above.
So, the essence of the dialectic is a real-time, interactive conversation between actual people (the dialectic cannot be done via books, or by one person). Its objective is to test knowledge. Its 'method' is that there is no constraint on the topic being discussed. Any theme may be introduced and any line of enquiry may be followed-up.
Dialectic supposes knowledge to be as located in a generative understanding and ramifying out through innumerable specific topics like branches and twigs from the trunk of a tree. Dialectic questioning moves between these specific topics at the twig ends, and follows back each answer through the larger branches and toward the central trunk (or real understanding, which itself cannot be directly observed).
Thus the dialectic represents a very ancient form of discourse, in which wisdom was understood only to be communicable and testable via direct, here-and-now, one-to-one (or one to just a few) human communication; and in which we can only know that someone else knows via real time and unstructured communication.
This is how the Master knows that his apprentice really understands the subject - and how a potential apprentice such as Socrates might evaluate a putative Master - and this is why all early university tests were simply discussions: 'oral', viva - or more fully viva voce = 'living voice' exams.
The dialectic 'method' is simply a thematic but unstructured conversation. That is why it is difficult for moderns to grasp the nature of dialectic; since moderns typically deny the necessity of the unstructured individual relationship in real education, testing and evaluation of understanding.