"The Waste Land" by T. S. Eliot is one of the touchstones of modern poetry; it may even be the most widely-known modern poem. Its style and content both reflect the literary movement of modernism. A few features that I will focus on in my answer are fragmented style, allusions, and tone.
First of all, modernist literature is known for its fragmented forms. The modernists tended to break from traditional forms of writing and invent new forms or, at the very least, break or fragment more common forms. "The Waste Land" is a long poem made of five titled sections. Within these sections, there is no consistent rhyme scheme or meter, so we can refer to this style as free verse. The sections are not consistent in terms of length, either. In other words, there is not a set form. Many modernist works focus on psychology or the inner world of characters or speakers rather than traditional narrative. We could not call "The Waste Land" a narrative or story in the traditional sense.
Allusions are an interesting feature of modernist literary works because the modernists believed in Ezra Pound's motto "make it new." So, you might ask how referring to older works of literature or to the Bible or mythology could be in any way new. Eliot is probably the modernist poet who most references classical texts in his work, and many readers need either a very experienced background in literature or some detailed footnotes to get through his works, especially "The Waste Land." One way to look at this conundrum is to think that in order for writers to break with the old and "make it new," they have to first know their literary history. Eliot certainly knows his. We can see in his varied and numerous references to classical Greek myth and tragedy (Tiresias in Part III), to Shakespeare, to Carthage and Phoenicia, and so on, that Eliot is well-versed in the classics. He does, however, put a modern spin on these texts through his allusions. Take the allusion to Tiresias, for example: Tiresias, the blind prophet from the ancient Greek tragedy Oedipus Rex, is described as an androgynous figure who can "see" into the dissatisfied and dingy lives of modern Londoners. It almost seems like a "waste" of the prophet's powers: what is there to observe here?
Finally, the tone of the poem is consistent with the mood of the modernist era. After World War I, Europeans certainly lost faith in some of the more solid and reliable facts of their world. It felt as though their world fell apart in a sense. How does one go on after that kind of loss and trauma? Eliot begins the poem with the famous line, "April is the cruellest month . . ." and that is our first clue, along with the title, that the poem will be dark and dour. We normally associate springtime with rebirth, happiness, fresh starts, and beautiful scenery. Here, Eliot subverts that expectation in a way that reflects the modernists' perspective on the post-World War I world.