I think there are two primary references in dealing with this subject; Hegel's Logic and the chapter on the method of political economy in Grundrisse. I think Marx either consciously borrowed or was heavily influenced by Hegel's method in Logic, and used the example of analyzing a given country starting with its population in showing how to apply Hegel's method in doing social science. (In this respect, I totally agree with Lenin in insisting that without reading Hegel's Logic one barely understands Marx's Capital, and that the latter is the best application of the former.)
Notice that the conceptual proceed of 'Being - Essence -Notion' in Hegel's Logic corresponds that of 'chaotic concrete - thin abstract - concrete with many determinations' in Grundrisse. We could also compare logical developments in Capital such as 'commodity - money - capital' or 'exchange value (immediately perceived) - value (as underlying essence) - exchange value (conceived in thought as form of appearance of value)' ('homology thesis', an argument that there is an one-to-one correspondence between Hegel's system and Marx's system. Of course the concrete correspondence is different from scholars to scholars. For example some argue that the category of 'capital' in Marx corresponds to that of Essence, not of Notion, in Hegel, excluding Notion from homology.)
First on Hegel's Logic: Hegel starts his Shorter Logic with mentioning how difficult it is to begin in doing philosophy. Here's what he says.
"But with the rise of this thinking study of things [i.e. philosophy], it soon becomes evident that thought will be satisfied with nothing short of showing the necessity of its facts, of demonstrating the existence of its objects, as well as their nature and qualities. Our original acquaintance with them is thus discovered to be inadequate. We can assume nothing and assert nothing dogmatically; nor can we accept the assertions and assumptions of others. And yet we must make a beginning: and a beginning, as primary and underived, makes an assumption, or rather is an assumption. It seems as if it were impossible to make a beginning at all." (Hegel's Shorter Logic §1)
Yet, we have to start anyway and the first mode of knowledge we form in our mind is concrete and empirical image established through empirical observation. However, Hegel criticizes empirical science, empirical knowledge for its shallowness and being contained in sense-perception, and argues that knowledge should be pursued beyond. But, he does not reject it all together but incorporates it within the totality of history of philosophy as an element constituting the latter. (This is a superior aspect of Hegel's 'wholistic' systematic philosophy.)
On the other hand, however, Hegel's system of Logic starts not with something empirical, i.e. something concrete-complex but with the category of Being, which is something abstract-simple, and which can be obtained (from the initial empirical perception) through some sort of thought process, i.e. reflection, and proceeds towards more concrete-complex categories, Essence and Notion. Then what is Hegel's true starting point; the concrete-complex empirically given or the abstract-simple?
Before answering this question, notice that there are two movements working in Hegel's system: First from the empirical concrete-complex to abstract-simple, and the second from the abstract-simple to the concrete-complex. Hegel calls the first movement the Analytical Method and the second the Synthetic Method (for definition of each refer to Hegel's Shorter Logic §227and §228).
From this we could easily figure out that there should be two different starting points in Hegelian logic for two different Methods; 'the point of departure in reality' for the Analytical Method and 'logical starting point' for the Synthetic Method.
(will be back with 'On Marx's Method 2'....)