Answer

Unfortunately, I don’t have time for that.
So as not to leave the page blank, and out of affection for holy matters, I’ll just tell you a few worthwhile things. I’m not sure I have an approach or a method that one needs to, or even can, learn. Maybe scholars of my thought will be able to find such a method in my writings. I don’t work with a fixed method; rather, each time I go according to what seems reasonable and sensible to me. I learn fairly close to the accepted yeshiva method, and certainly on its basis. But with additions and subtractions: additions in examining what the root of the reasoning is and what its broader philosophical and meta-halakhic implications are, and subtracting things that aren’t logical (even though they’re part of the yeshiva-style repertoire), as well as neutralizing overlaps (when two lines of reasoning are really just two ways of saying the same thing, with practical differences). And finally, in quite a few cases I also allow myself to formulate a position—that is, to decide who is right, or which side of an analytical inquiry is more plausible (something yeshivot are careful not to do).
This discussion reminds me of a conversation I once had with my shiur teacher in Netivot Olam. I came to him and told him that the Chazon Ish and the Sema were difficult for me. Their words seemed to me like those of ordinary householders (as opposed to the Ketzot HaChoshen, Rabbi Chaim, Rabbi Shmuel, etc., who were “lamdanim,” analytical Torah scholars). He told me then that it was all a matter of how things are presented and the form of analysis. And indeed, I later understood that if you analyze the Sema and the Chazon Ish in the yeshiva way, they too can “become” yeshivish.
I was reminded of this because it seems to me that what distinguishes those two (the Sema and the Chazon Ish) is that they didn’t have a method. Each time they said what seemed reasonable to them in that particular context, and they didn’t force things into a method. When someone else, who does have a “method,” analyzes them, he of course discovers a method in them. At that point you can wonder whether that method is theirs or his. It is something like the well-known debate between the Seridei Esh and Rabbi Yehoshua Hutner (one of the editors of the Talmudic Encyclopedia) regarding Rabbi Chaim: did he understand Maimonides (that is, uncover Maimonides’ “method”), or did he invent a Torah of his own (that was his “method”)? By the way, I personally think that in many cases he understood very well, but formulated the ideas in his own language and in his own mode of analysis. And sometimes one can say about him what Rabbi Kook wrote in the eulogy for the Sochatchover that he sent to his grandsons: the Talmud says that Rabbi Eliezer did not say anything he had not heard from his teacher, and elsewhere we find that he said things that no ear had ever heard before. The resolution is that he heard from his teacher things that no ear had ever heard before (and I would add: including his teacher’s ear). In my view, that isn’t a clever quip but the absolute truth. I myself heard from my shiur teacher things that he himself did not agree with, and I still think I’m right and not he—that is, that I understood him better than he understood himself. And of course, the formulation I gave those ideas was my own and not in his language.
All the best and much success,