You need to start out by reading the poem through twice. First, read for ‘content’: what is the situation, who are the characters, what is going on, what are the events and relationships that are happening? You should, after this reading, be able to write a sentence that says what happens in the poem.
Next, read for ‘form’: what does the poem look like on the page, and what does it sound like when you read it aloud? Do any lines stick out because of the way they sound? There are a lot of ways of thinking about form—things like metre, rhyme scheme, assonance and consonance, rhetorical figures—and you should look into some of these that interest you, and use them to start building your own language for talking about poetic form.
Now you have an idea of the poem’s content and form, go through, line-by-line, underlining and making notes about how those two things interact. Does a rhyme link together two words in an interesting way? Is there heavy assonance at a moment of particular emotional importance? What does the choice of metaphor or simile say about the object or person it refers to? Are there comparisons to be made with other poems you know?
Look for anything you find interesting. You are not being asked to find any specific feature, only to write about the things that you find interesting. Two close readings of a poem might both be equally good, but mention none of the same points as one another.