From reading a selection of writings by Marx, I have come to understand the following three as the core elements of Marxian economics.
The labour theory of value. It asserts that the exchange value of a commodity $x$ (what quantities of $x$ that can be exchanged for another commodity) is determined by that labour time which is socially necessary to produce $x$.
Surplus value theory of profit. I.e., capitalists derives profit from their exploitation of workers. Suppose a capitalist purchases labour power from a worker for one day. To Marx, then, the value of one day's usage of this labour power is the value of the commodities which is necessary for the worker to live through one day. Say that it takes one fourth of a day to produce this amount of commodities, the value of which will be equivalent to the wage paid to the worker by the capitalist. This one fourth of a day is called necessary labour. Any work above this level is surplus labour from which the capitalist derives profit.
The theory of alienation. In the following I quote a passage from Marx's Economic and Philosophical Manuscripts of 1844. Relating this passage to the above core elements, I note that Marx somehow seems to think that the institution of capitalism structures parts of the social world.
The worker becomes poorer the more wealth he produces, the more his
production increases in power and extent. The worker becomes an ever
cheaper commodity the more commodities he produces. The devaluation of
the human world grows in direct proportion to the increase in value of
the world of things. Labour not only produces commodities; it also
produces itself and the workers as a commodity and it does so in the
same proportion in which it produces commodities in general.
This fact simply means that the object that labour produces, its
product, stands opposed to it as something alien, as a power
independent of the producer. The product of labour is labour embodied
and made material in an object, it is the objectification of labour.
The realization of labour is its objectification. In the sphere of
political economy, this realization of labour appears as a loss of
reality for the worker, objectification as loss of and bondage to the
object, and appropriation as estrangement, as alienation.
So much does the realization of labour appear as loss of reality that
the worker loses his reality to the point of dying of starvation. So
much does objectification appear as loss of the object that the worker
is robbed of the objects he needs most not only for life but also for
work. Work itself becomes an object which he can only obtain through
an enormous effort and with spasmodic interruptions. So much does the
appropriation of the object appear as estrangement that the more
objects the worker produces the fewer can he possess and the more he
falls under the domination of his product, of capital.