William Carlos Williams kicked off his poetic career as part of the Imagist movement, a school of poetry headed up by his buddy Ezra Pound. This movement's main goal was to paint precise images without using a bunch of fancy shmancy words that just get in the way of what a poem is trying to describe. The Imagists wanted to keep it simple, but keep it real. You can totally see the influence of this movement in the opening stanza of "The Last Words of My English Grandmother." Check it out:
There were some dirty plates
and a glass of milk
beside her on a small table
near the rank, disheveled bed— (1-4)
Williams uses nothing but simple words here. There are no high falutin' poetics. He's just giving us precise details that come together to make a vivid picture in our minds of the gross state of the grandmother's sickroom. Though the Imagist movement was over by the time he wrote this poem, you can see its influence in it and a bunch of his other poems as well.
Later in his career, Williams got all psyched about creating a uniquely American style of poetry, one that represented the lives and language of everyday people in the U. S. of A. Even though this poem is about an English grandmother, you can see the influence of this style here for sure. The third stanza is a great example:
Gimme something to eat—
They're starving me—
I'm all right—I won't go
to the hospital. No, no, no (9-12)
See how casual and conversational it feels? Williams even goes so far as to include the slang word, "Gimme" (3.6). This granny might be English, but she seems kinda American to us. The language and rhythms of the poem totally reflect everyday speech, just like Williams wanted them to.
For more examples of his style, check out "The Red Wheelbarrow" or "This is Just to Say."