First, you should narrow this down, or if the assignment calls for a summary of 20th century poetry, you should identify the different kinds or movements of poetry throughout the century and it would also help to know if this is specific to a certain area of the world or a particular country.
The century can be broken down into the two larger historical periods of Modernism and Postmodernism.
From a Western perspective, within the overall Modernist period (which takes place from about the late 19th century through the early to mid 20th century), you would have to discuss Imagism (Pound, Williams, etc.), Symbolism and maybe even Futurism – these three being prominent artistic movements at the beginning of the 20th century. Getting closer to WWII and its aftermath, there are the Beat Poets, the experimental L=A=N=G=U=A=G=E poets, Black Mountain Poets other more politically charged poets during the Civil Rights movements of the 1960s (in America; Ginsberg, Burroughs, etc.) and this period overlaps with the Postmodern era with examples such as Charles Bukowski and Amiri Baraka. So, as far as your essay is concerned, I would either choose one movement (i.e. The Beat Poets) if you can do that. If the essay has to be a general summary, break it down and focus on these groups (or others if you want), just as a way to structure the essay. Note each groups objectives, style and subject matter and see if there are similarities/differences as you go along. If it is a comprehensive essay about the entire century, start with the Imagists.