Peter Leithart has a post about method.
Jean-Luc Marion points out that "method" comes from the Greek meta+hodos, and explains why phenomenology is not methodological: "The method does not run ahead of the phenomenon, by fore-seeing it, pre-dicting it, and pro-ducing it, in order to await it from the outset at the end of the path (meta-hodos) onto which it has just barely set forth." Conversely, philosophy influenced by Descartes is governed by method, which means that all its conclusions were determined at the outset. Methodological philosophy (and its cousin prolegomenal theology) knows from the beginning where it is headed; it immanentizes the eschaton.
Apart from coming near to the etymological fallacy, it seems that Marion (and perhaps Leithart) have left out of consideration the multiple meanings of the Greek word meta. Marion's analysis indicates that he thinks meta means "after"; this is the meaning of the preposition in the title of Aristotle's Metaphysics: the work Metaphysics is so named because in the traditional Aristotelian corpus it was placed after the work Physics.
The problem with Marion's clever point is that meta can also mean "with." (When paired with the accusative case, meta means after; paired with the genitive case, it means with.) Given our common-sense notion of method, it seems more likely that meta means with, so that meta + hodos = "with a way." The ancient (Homeric) meaning of method is "pursuit." To this is added, by the philosophers, especially Plato, the meaning of a principled way of proceeding. (Note that hodos means way or path.) The point of method is not that it determines or knows everything ahead of time (and so can wait at the end of the path (of experience?) but that it provides us an organized (to mix in some Latin) way of moving through the world.
Leithart says that "philosophy influenced by Descartes is governed by method, which means that all its conclusions were determined at the outset." If I understand aright, he means that philosophy influenced by Descartes is deterministic in the sense that the principles (or, conclusions) of that philosophy are set down in stone by the method. But for Descartes especially (and maybe Leithart does not include Descartes in those "influenced by Descartes"), method is the harmonious way of moving through the rational structure of the universe in order to discover the truths about the universe. It is harmonious because it requires the "methodist" to take what the world gives and not invent or tear the world. It is necessary because it is the only way that we can be sure that our conclusions are true. A careful reader of the Meditations will, I think, realize that Descartes's insistence on following the method is for just that purpose.
Aside: for some reason (perhaps it's Gilson?), Descartes is the whipping boy for many people today. Most of those who beat him show only a surface familiarity with him. Further, Leithart's association of method with Descartes is not completely accurate. After all, method is from the Greek methodos, which figures prominently in, among other ancient works, Plato's Sophist and Statesman.
Leithart then says that "Methodological philosophy (and its cousin prolegomenal theology) knows from the beginning where it is headed," which is false. Presuming it's safe to substitute "methodological philosophers" for "methodological philosophy," it seems that Leithart has mixed ontology with epistemology. It is precisely because we do not know what the conclusions are that we must adhere to some method. Without method, according to Descartes, we have no way of knowing what the world is like. We might as well make it up as we go along.
Now, I am not saying that phenomenologists like Husserl (or Marion) make it up as they go along. But they do have a method; it just might not be the Cartesian one.
Slightly related point: I have a friend who once had a bumper sticker with an allusion to the quotation (to which Leithart refers in his last sentence) from Eric Voegelin: "Thou shalt not immanentize the eschaton." (Actually, the quotation from Voegelin is "When the attempt is made, first merely in principle, to immanentize the transcendent eschaton (in the Christian sense of the term), then everything follows from the logic of the approach, right down to the historical fact as the answer to the meaning of self-interpreting existence" [Faith and Political Philosophy, p. 73].) It seems that Voegelin's point is also related to some kind of fixity ("everything follows from the logic of the approach"), but I don't know Voegelin at all and so can't say anything about that.