Thumbnail is Marx's manuscript for The German Ideology. Summary below is a compilation of my notes I wrote when reading Materialism and the Dialectical Method by Maurice Cornforth, along with general knowledge from reading various Marxist authors.
Often times, Marxists use the term "material conditions," and "dialectics." What does this mean? Why do Marxists care so much about material conditions? The answer is that Marxists seek materialist explanations for observed processes as opposed to idealist, and do so dialectically, as opposed to metaphysically. In other words, Marxists apply dialectical analysis to find materialist explanations for phenomena. Dialectical materialism is the world outlook of the proletariat as a class, and serves as the most vital ideological tool for overthrowing capitalism.
In order to understand dialectical materialism, we need to understand its component parts, materialism and dialectics, and their historical predecessors, idealism and metaphysics.
Idealism

Idealism is, in short, to put ideas prior to matter. Idealism has been used by feudal lords to justify their position above the serfs, forming the ideological basis for feudalism. The 3 major assertions of idealism are as follows:
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Idealism asserts that the material world is dependent on the spiritual
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Idealism asserts that spirit, or mind, or idea, can and does exist in separation from matter. (The most extreme form of this assertion is subjective idealism, which asserts that matter does not exist at all but is pure illusion.)
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Idealism asserts that there exists a realm of the mysterious and unknowable, "above," or "beyond," or "behind" what can be ascertained and known by perception, experience, and science.
Early Materialism

Common idealist arguments are appealing to a supernatural "human nature," or "good vs. evil" explanations for processes. Materialism arose over time, as people grew to understand the world more deeply, and especially as a tool to overthrow the feudal aristocracy that justified its existence via the church. In other words, materialism rose to help the bourgeoisie. The 3 basic teachings of materialism as counterposed to idealism are:
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Materialism teaches that the world is by its very nature material, that everything which exists comes into being on the basis of material causes, arises and develops in accordance with the laws of motion of matter.
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Materialism teaches that matter is objective reality existing outside and independent of the mind; and that far from the mental existing in separation from the material, everything mental or spiritual is a product of material processes.
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Materialism teaches that the world and its laws are fully knowable, and that while much may not be known there is nothing which is by nature unknowable.
Shortcomings of Metaphysical Materialism

The type of materialism that overthrew the feudal lords was still underdeveloped, and metaphysical. The bourgeoisie needed an explanation for why the feudal lords were illegitimate, but still needed to support their own static, permanent rule. This was called mechanistic materialism, for the bourgeois scientists saw the world as a grand machine repeating simple motions forever. Mechanistic materialism, therefore, makes certain dogmatic assumptions:
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That the world consists of permanent and stable things or particles, with definite, fixed properties;
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That the particles of matter are by nature inert and no change ever happens except by the action of some external cause;
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That all motion, all change can be reduced to the mechanical interaction of the separate particles of matter;
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That each particle has its own fixed nature independent of everything else, and that the relationships between separate things are merely external relationships.
Moving from Metaphysics to Dialectics

This, of course, has proven false. History did not end with the dissolution of the USSR, despite what modern mechanistic materialists claim. Mechanistic materialism relies on metaphysics, seeing everything as a static abstraction, devoid of its context. It has no explanation for how new qualities emerge, and ultimately fell to idealism to explain the "first mover," ie "God." Dialectical materialism holds instead:
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The world is not a complex of things but of processes;
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That matter is inseperable from motion;
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That the motion of matter comprehends an infinite diversity of forms which arise one from another and pass into one another;
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That things exist not as separate individual units but in essential relation and interconnection.
Dialectical Materialism

This became remarkable for the proletariat, as it sees nothing as static, and therefore marks the eventual downfall of the bourgeoisie. Putting it all together, we get the following:
- Dialectical materialism understands the world, not as a complex of ready-made things, but as a complex of processes, in which all things go through an uninterrupted change of coming into being and passing away.
In other words, when analyzing events and contextualizing them, we must always viee them as a struggle between the rising and the falling, the old and the new, for example the concentration of capital in markets and the rise in socialize labor.

- Dialectical materialism considers that matter is always in motion, that motion is the mode of existence of matter, so that there can no more be matter without motion than motion without matter. Motion does not have to be impressed upon matter by some outside force, but above all it is necessary to look for the inner impulses of development, the self-motion, inherent in all processes.
In other words, all movement is a result of contradiction. Your foot presses on the Earth, and the Earth presses back on you.

- Dialectical materialism understands the motion of matter as comprehending all changes and processes in the universe, from mere changes of place right to thinking. It recognizes, therefore, the infinite diversity of the forms of motion of matter from the simple to the complex, from the lower to the higher.
In other words, dialectical materialism recognizes that development exists as a change of quantity into quality. Addition or subtraction gives way to qualitative change. A balloon is filled with air, until at a given point it pops due to pressure buildup. Water goes from liquid to gas at its boiling point, and back into liquid when cooling down to said point.

- Dialectical materialism considers that, in the manifold processes taking place in the universe, things come into being, change and pass out of being, not as separate individual units, but in essential relation and interconnection, so that they cannot be understood each separately and by itself but only in their relation and interconnection.
In other words, everything is connected, and must be analyzed in context to truly understand it. A worker isn't just an individual, but instead part of a social class of many workers. Wages are not something invented brand new every time, but instead are set by societal standards, controlled by the ruling capitalist class.

Conclusion
Karl Marx created dialectical materialism by turning Hegel's idealist dialectic into a materialist one. Then, he applied it to the progression of society, creating historical materialism. By analyzing social structures and progress as a dialectical process based in materialism, we can learn from history and analyze where it's going. This is scientific socialism in progress. Human thought is shaped by our social experience, forming class consciousness and ideology. How we produce and distribute determines our ways of thinking.
Socialism and communism also have their own contradictions as well, and just because we progress on to socialism does not mean we cannot fall back to capitalism. The dialectical materialist world outlook understands that nothing is static, and there is always new contradiction and new movement from that.
If you keep these in mind, you can do your own dialectical materialist analysis. Always seek explanations based on the material, not the ideal, and always do so by contextualizing the processes, analyzing their contradictions, the unity and struggle of opposing tendencies. Quantitative changes lead to qualitative development, and progresses as a result of the conflict or struggle of opposite tendencies. There's much more to dialectical materialism, but this should help serve as a simple overview!
An example of metaphysical idealism can be found in @PugJesus@piefed.social's post Here, on Piefed.social's History Memes community. Here is the post in question:
And here is the context provided by PugJesus below, in full:
Let's break this down.
Nobody makes this point. Marxists seek to understand and explain why socialists made the decisions they've made. The reason for this is so that we can learn the true causes, understand the decisions made, and thus learn from their mistakes so as to not repeat them, while learning from their successes so as to apply when possible.
The reason this is metaphysical and idealist is because the topic of the post, population transfer of Koreans, happened during the period of World War II, both its build-up and during the war itself. Paranoia was at an all-time high in the soviet union, and Koreans were suspected due to the highly reactionary dictatorship Japan had installed there as a part of their colonial project. As such, the soviets decided to forcibly relocate 170,000 Koreans from the far-east of Russia to Kazakhstan and Uzbekistan.
For PugJesus, the reason for this is unstated, and context does not exist. The only explanation left for PugJesus is just "soviets did it because they were evil." Not only this, but PugJesus therefore makes the strawman that Marxist-Leninists believe that every misstep of the soviet union was actually necessary and unavoidable. Population transfer is one of the most universally accepted mistakes of the USSR by most Marxist-Leninists, with some exceptions, but because we are dialectical materialists, we seek root cause analysis.
The handling of the Koryo-Saram was a deep tragedy and mistake. It was not necessary for "building socialism," despite what PugJesus believes Marxists think, nor was it done as a deliberate act to wipe out ethnic Koreans. It was a deeply flawed handling of a percieved problem based on real threats from Japan.
This line of argument is dubious because it does not exist. Nobody defends literally everything the soviets did, we seek to understand their achievements and mistakes in context, and the underlying causes. Further, the "genocide" and "ethnic cleansing" is left open, here.
Debatable, especially considering the strawman PugJesus made of Marxism-Leninism in general and dialectical materialism in particular.
The interesting bit here is that PugJesus says the CNT-FAI made a "mistake" by imprisoning criminals and fascists, because of an idealist "moral code." The reason the CNT-FAI developed prisons over the course of the war was because they learned that they needed them in the context of war, even if they sought to abolish them afterwards. This is an example of anarchists adjusting their theory after it ran into problems in reality, adjusting to it, and becoming more effective as a consequence.
By understanding the context of the prisons, ie a brutal war, and their material causes, having a ton of fascists and criminals during the brutal war, we can see that this was a necessary step. By contrast, when analyzing the population transfer of the soviets, we have to question what may have happened had they focused directly on cracking down on infiltration of Japanese spies in the far-east of Russia, rather than relocating the entire ethnic group.
It's more reasonable when contextualizing the population transfer to recognize it as a mistake, but not one made out of a supernatural "evil," and not one made for no reason, but due to deep suspicions on the eve of war. It was not necessary to handle the threat of espionage in this manner, and a number of other courses could have been taken. This is a mistake to learn from, while the prisons employed by the CNT-FAI were a strategic advancement on previous anarchist theory when waging open war.
Dialectical materialism allows us to identify root causes. It is not the answer to any particular question, but tells us where to look and how to do so. This is the weakness of bourgeois historiography, the erasure of context and analyzing events and history as a "series of static snapshots" rather than an unfolding process leads to dramatic errors.
Note: replying here rather than on PugJesus' post itself, because both PugJesus and Deceptichum ban Marxism and Marxists.
Why was having prisons a necessary step?
What is colloquially referred to as ''evil'' can be explained in plain material terms: people in power often do not care about the ethical or human consequences of their actions, and so they do not have reason to prioritize the health and wellbeing of their victims.