Read through the poem several times. Look for images and sounds. Think about what emotional effect the poem had on you.
Read the poem out loud, looking for the rhythm of the poem. Look for the story in the poem. Determine who is speaking. Is it Lazarus or is she writing through the voice of a different narrator?
Learn about the history of both the Statue of Liberty and the Colossus of Rhodes. Look for parallels and differences between both statues.
Pay attention to the symbols in the poem and how they make you feel about this statue. Determine if Lazarus is depicting it with reverence or looking at it as a symbol of hubris.
Look up any words that you do not understand. Since poetry is about economy of words, knowing the definitions of all the word will help you understand and interpret the poem better.
Create your own hypothesis of the poem's meaning. Reread the poem once more when your feel your interpretation is solid, looking for symbols and clues that you are correct.