How do you apply Marxist theory to the literature "no country for old man"?

I am not sure if your question concerns Yeats's "Sailing to Byzantium," of which "There is no country for old men" is the first line, or the Coen Brothers' film which uses Yeats's verse for its title. If you mean the poem, I would offer the following suggestions:
Marxian ideas can be seen in the basic message of the poem that materialistic values are ephemeral or false. The speaker indicates that

An aged man is but a paltry thing,A tattered coat upon a stick, unlessSoul clap its hands and sing, and louder singFor every tatter in its mortal dress

One knows that the material world will pass away, and that the spiritual realm, the realm of the soul, is the only thing that matters. The speaker says his heart is

sick with desire,And fastened to a dying animal,It knows not what it is;

The "dying animal," the body, is a mere shell, in itself worthless and perishable, and it is only through song, through the spiritual nature of man, that one lives on, becoming part of the "artifice of eternity." Why, one might ask, is it an "artifice" to which the poet refers? One could argue it's because man himself creates the possibility of become timeless and infinite, through his work, or through his art, like that of the form the "Grecian goldsmiths make."
To Marx, the accumulation of material wealth, of capital, for its own sake is a self-destructive process. The basic idea can be applied to the anti-materialist vision of Yeats's poem. A further link with Marxian thought can be seen in the poem's rejection of the past, expressed in the famous opening line. A country "not for old men" would be one in which older values must necessarily be swept away, replaced by the new in a ceaseless process in which the elements of life and of nature

commend all summer longWhatever is begotten, born or dies.

In Marxian thinking, each "dying generation"—"dying" because death is simply a part of the world-process, of renewal as well as of ending—must be free to determine its course, instead of forever having to preserve the way of doing things dictated by the past. The speaker wishes to sing to the "Lords and Ladies of Byzantium"—the lords and ladies of the spiritual, not material, world—

Of what is past, or passing, or to come.

My interpretation probably is open to criticism if viewed in the context of what we know of Yeats's own political orientation. You might wish to research this or see if other poems of his can be read as expressing my points made above. George Orwell, in his essay on Yeats, described the poet's writings as embracing a longing to return to an almost medieval social hierarchy. Though Orwell goes so far as to use the term "fascist" in this context, perhaps we can invoke the truism that it's a sign of a poet's greatness that his work is open to many, even contradictory, interpretations.