Choose a poem. You can choose any poem you like, but usually this depends upon the assignment.
Read the poem several times slowly. Even read it aloud. Poetry is meant to be read and reread, and odds are you won't catch all the small details the first time around. Take diligent notes and record your ideas as you read it, highlighting important lines.
Study up on the author and time period. Learning about the poet can give you an idea of what he was thinking when the poem was written. Knowing the era can help you understand what was going on in the world at the time and what may have inspired the piece.
Continue rereading the poem as you research and study its history. Eventually you should have enough notes to support your analysis.
Write your analysis, supporting your points with the research you found and passages in the poem. Explain why the poem is about a certain thing using other people's research and citing it properly.