The first thing I encourage my students to do when reading a new poem for the first time is to read it once to get a sense of the entire text and where it is leading, and then to read it one more time to get more of the details and understand their place within the whole.
Next, I ask them to paraphrase the poem, translating figurative language into more literal language—for example, metaphors are rephrased as similes. We find that changing the poem's words into your own words is really helpful in terms of understanding its meaning.
Next, we try to work out the poem's general meaning based on the paraphrase. We also identify any poetic devices—metaphors, symbols, similes, personification, and so forth—and try to figure out how they contribute to the meaning of the poem.
Sometimes, if the poem is particularly confusing, we might start by identifying the connotations of the words and the mood of the poem. This helps us to work out meaning too.
Answer an exam question about a poem by addressing a series of topics. First, you should identify the author and approximate date of the poem. Next, you might discuss whether the poem belongs to or is typical of a specific literary movement (Romantic, Augustan, etc.) and identify its genre (satire, ode, epithalamium, etc.). Next, summarize its main prosodic features (rhythm and rhyme scheme). Next you should discuss its literary style and use of poetic devices or figures of speech. Then you should mention its narrator or narrative voice and main subject matter or themes. You should also note allusions to other poems.