I'll try.
Dugin analyzes what he identifies as the three main political ideologies of the last 150 years: Liberalism, Fascism/National Socialism and Marxism. Out of these three Liberalism emerged victorious, and the 4th political theory, that he tries to evolve (National Bolshevism), must be ultimately contrarian to what the ruling ideology, liberalism, encorporates - it must appropriate the useful parts of both Fascism and Marxism ("reading Evola from the left and Marx from the right") but can't be afraid to discard the negative elements of both or add new concepts to it. The 4th political theory, which might emerge or not, is not yet pressed in a dogmatic costume, and intellectuals of both left and right are welcome to contribute.
Liberalism, the victorious ideology, has the individual as its subject. Within this, there is a contradiction, because once it defeated the competing ideologies of Fascism and Communism, it rendered itself meaningless as a dogma. In the victory of liberalism is the key of its own destruction. We are now living in the post-ideological era, with "human rights", "property rights" and the "free market" as the universal values that are protected. It doesn't matter anymore if a politician is left or right, politicians are problem solvers, managers in an apolitical environment: Dugin calls this "micromanagement". We are living in a world of micromanagement where political ideology is replaced by technocracy. Therefore, to be contrarian, National Bolshevism must reject said core values of human rights, property rights, individualism and the free market. Liberalism is also inherently racist and chauvinistic, as it assumes it's core values are universally right, globally applicable and have to be implemented into every culture on earth, and when they are not, a culture or a system will be insulted as backwards.
He says liberalism has a very unnatural core by demonizing the past, while every other culture respects the past or their ancestry. Liberalism believes in the irreversability of time and the 4th political theory must belive in the reversabilty of time. Also, while every other culture felt guilt by accumulating wealth, and atoned for that by sacrificing riches on altars, liberalism fetishizes wealth. By sacrificing riches humanity experiences a katatonic purification and event where time is reversed. Contradictions will lead to the point where the nihilistic dialectic of liberalism will collapse, reverse, and humanity will come into "being" again - this is highly influenced by Heidegger. Out of this, Dugin draws the conclusion of what has to be the subject of National Bolshevism: "Being".
Furthermore, National Bolshevism must start by borrowing elements of the two defeated ideologies, Fascism and Communism.
Fascism and Not Socialism are a little different from Liberalism and Communism as they were killed in their cribs - for this, Dugin blames Not Socialism since it was doomed to fail because of its open and disgusting racism. Fascism has "state" as its subject and Not Socialism has "race". However, Fascism (especially Italian) has the advantage of combining Futurism and Traditionalism into a synthesis that elevates it to being relevant and realistic. The fact that it doesn't just aesthetizise poltics, but politicizes aesthetics, is contrarian to technocracy and must be harvested.
Marxism (it's subject is "class") is more useful than Fascism - it shines at analyzing it's enemy, liberal capitalism, with its merciless empirical analysis. It imploded into itself due to a contradiction between its brutal modernism and nihilism and it's prophetic core. He claims that communism in its core promises an utopia not unlike the bible and is therefore anti-modern in its character; that's a good thing. It's econimic analysis, organisation of institutions that are democratic but anti-parliamentarian and prophetic value shall be central to National Bolshevism but it's Internationalism and moral relativism must be discarded.
As an outlook, Dugin suggests Russia as the birthplace of the 4th theory, since it's by its very nature a contrarian civilisation since it's inception, even though currently capitalist it's inherently opposed to liberalism. What should be strifed for is an Eurasian awakening, respecting the diverse cultures within its borders without multiculturalism but pluralism, an alternative economic order and the ultimate rejection of liberalism in a pan-nationalist state.
Sorry for my bad English I'm Kraut and also typed this on a train.