As for the idea of "dialectic", Marx got it from Hegel, and a full understanding of Hegel -- if it is possible at all -- is not something that can be effectively communicated in a comment or short internet article, I think.

I think David Stove did a pretty good job. :)

As a rough approximation, though, the dialectical method is basically just systems thinking.

I've never understood what that is either, even though I work with "systems biologists". I don't see a distinction drawn between "systems biology" and just "biology".

"Dialectical materialism" in Marxist thought is basically just an application of this dialectical thinking to economics. One could approach economics analytically by first, say, constructing a model of individual economic agents, and then trying to figure out what happens when these agents interact under certain conditions.

That is, microfoundations for macroeconomics. This appears to be a disputed idea in macroeconomics, some arguing that microfoundations are essential, others that they are impossible.

The natures of individual elements are constituted by their participation in the system, and they change as the system evolves, so you shouldn't treat those individual natures as logically prior to the system.

When I try to translate this into concrete terms, I start imagining chemists arguing that you can't understand molecules in terms of atoms, because atoms can change their ionisation state when they combine into molecules.