Understanding the actual text of the poem is not hard at all. There aren't any long, weird SAT words, the poem's literary references are folded into normal, everyday speech, and the occasional cultural references are easy enough to Google.
So, where does the poem's difficulty lie? In all the things left unsaid. Don't forget that the poem is called "Silence," and, here, silence is meaningful. We have to spend some time figuring out what the speaker suggests or implies but doesn't quite put into words. For example, why doesn't the speaker say anything about herself? What can we figure out about her anyway? Why does she let her father's words take up most of the poem? What is her attitude toward what he says?