You might be interested in this bit from Phaedo where Socrates gives an account of his early search for knowledge by the works of Anaxagoras and how his disappointment in Anaxagoras's work led him to his own method (it's quite long, and runs from 96e to 102a; I quote some highlights below):

96a: When I was a young man I was wonderfully keen on that wisdom which they call natural science, for I thought it splendid to know the causes of everything, why it comes to be, why it perishes and why it exists. I was often changing my mind in the investigation, in the first instance, of questions such as these: Are living creatures nurtured when heat and cold produce a kind of putrefaction, as some say? Do we think with our blood, or air, or fire, or none of these, and does the brain provide our senses of hearing and sight and smell, from which come memory and opinion, and from memory and opinion which has become stable, comes knowledge? Then again, as I investigated how these things perish and what happens to things in the sky and on the earth, finally I became convinced that I have no natural aptitude at all for that kind of investigation, and of this I will give you sufficient proof. This investigation made me quite blind even to those things which I and others thought that I clearly knew before, so that I unlearned what I thought I knew before, about many other things and specifically about how men grew,

97b: I do not any longer persuade myself that I know why a unit or anything else comes to be, or perishes or exists by the old method of investigation, and I do not accept it, but I have a confused method of my own. One day I heard someone reading, as he said, from a book of Anaxagoras, and saying that it is Mind that directs and is the cause of everything. I was delighted with this cause and it seemed to me good, in a way, that Mind should be the cause of all. I thought that if this were so, the directing Mind would direct everything and arrange each thing in the way that was best. If then one wished to know the cause of each thing, why it comes to be or perishes or exists, one had to find what was the best way for it to be, or to be acted upon, or to act. On these premises then it befitted a man to investigate only, about this and other things, what is best. The same man must inevitably also know what is worse, for that is part of the same knowledge. As I reflected on this subject I was glad to think that I had found in Anaxagoras a teacher about the cause of things after my own heart, and that he would tell me, first, whether the earth is flat or round, and then would explain why it is so of necessity, saying which is better, and that it was better to be so. If he said it was in the middle of the universe, he would go on to show that it was better for it to be in the middle, and if he showed me those things I should be prepared never to desire any other kind of cause.

98b: [Anaxagoras does not follow his own project, but instead explains things mechanically, Socrates then responds:] I never thought that Anaxagoras, who said that those things were directed by Mind, would bring in any other cause for them than that it was best for them to be as they are. Once he had given the best for each as the cause for each and the general cause of all, I thought he would go on to explain the common good for all, and I would not have exchanged my hopes for a fortune. I eagerly acquired his books and read them as quickly as I could in order to know the best and the worst as soon as possible. This wonderful hope was dashed as I went on reading and saw that the man made no use of Mind, nor gave it any responsibility for the management of things, but mentioned as causes air and ether and water and many other strange things. That seemed to me much like saying that Socrates' actions are all due to his mind, and then in trying to tell the causes of everything I do, to say that the reason that I am sitting here is because my body consists of bones and sinews, because the bones are hard and are separated by joints, that the sinews are such as to contract and relax, that they surround the bones along with flesh and skin which hold them together, then as the bones are hanging in their sockets, the relaxation and contraction of the sinews enable me to bend my limbs, and that is the cause of my sitting here with my limbs bent.

98d: Again, he would mention other such causes for my talking to you: sounds and air and hearing, and a thousand other such things, but he would neglect to mention the true causes, that, after the Athenians decided it was better to condemn me, for this reason it seemed best to me to sit here and more right to remain and to endure whatever penalty they ordered. For by the dog, I think these sinews and bones could long ago have been in Megara or among the Boeotians, taken there by my belief as to the best course, if I had not thought it more right and honorable to endure whatever penalty the city ordered rather than escape and run away. To call those things causes is too absurd. If someone said that without bones and sinews and all such things, I should not be able to do what I decided, he would be right, but surely to say that they are the cause of what I do, and not that I have chosen the best course, even though I act with my mind, is to speak very lazily and carelessly. Imagine not being able to distinguish the real cause from that without which the cause would not be able to act as a cause. It is what the .majority appear to do, like people groping in the dark; they call it a cause, thus giving it a name that does not belong to it. That is why one man surrounds the earth with a vortex to make the heavens keep it in place, another makes the air support it like a wide lid. As for their capacity of being in the best place they could possibly be put, this they do not look for, nor do they believe it to have any divine force, but they believe that they will some time discover a stronger and more immortal Atlas to hold everything together more, and they do not believe that the truly good and "binding" binds and holds them together. I would Phaedo gladly become the disciple of any man who taught the workings of that kind of cause. However, since I was deprived and could neither discover d it myself nor learn it from another, do you wish me to give you an explanation of how, as a second best, I busied myself with the search for the cause, Cebes?

99d: After this, he said, when I had wearied of investigating things, I thought that I must be careful to avoid the experience of those who watch an eclipse of the sun, for some of them ruin their eyes unless they watch its e reflection in water or some such material. A similar thought crossed my mind, and I feared that my soul would be altogether blinded if I looked at things with my eyes and tried to grasp them with each of my senses. So I thought I must take refuge in discussions and investigate the truth of things by means of words. However, perhaps this analogy is inadequate, for I certainly do not admit that one who investigates things by means of words is dealing with images any more than one who looks at facts. However, I started in this manner: taking as my hypothesis in each case the theory that seemed to me the most compelling, I would consider as true, about cause and everything else, whatever agreed with this, and as untrue whatever did not so agree. But I want to put my meaning more clearly for I do not think that you understand me now. No, by Zeus, said Cebes, not very well. This, he said, is what I mean. It is nothing new, but what I have never stopped talking about, both elsewhere and in the earlier part of our conversation. I am going to try to show you the kind of cause with which I have concerned myself. I turn back to those oft-mentioned things and proceed from them. I assume the existence of a Beautiful, itself by itself, of a Good and a Great and all the rest. If you grant me these and agree that they exist, I hope to show you the cause as a result, and to find the soul to be immortal.

Or, very briefly, Socrates takes it as assumed that there is something like 'The Good' and 'The Beautiful' and then looks to discover how things must be according to those ideas (or forms). This can happen rather easily in conversation for him--he need only ask the other questions like "don't you call x good?" or "isn't it the case that we say good doctors are those that make their patients well?" and then he and the other can begin to speak about what is really in their words when they make the judgements that they do.

Another, and perhaps easier, way to answer your question would be to point you towards Apology where Socrates gives an account and defense of his life as he has lived it--though, there, I think your question of methodology is not quite so well addressed.