In her preface to her wonderful book The Angles of Light, Luci Shaw gives some great insight on how to read poetry. Here are a few of the points she makes, in her words:

• In the poem the writer has made a bridge, or half a bridge, across the watery expanse of understanding. The half-structure reaches toward your imagination from the poet's side. In order to join it, you, the reader, must extend the other half of the bridge from your side of the riverbank. You must take the risk of reaching toward the constructed work the poet offers you, and in meeting it, join it, so that the images, ideas, emotions, perceptions, music, and rhythm can flow from the poet's mind into your own.
• It's a journey into someone else's mind, into the unknown, into mystery. But as you move forward into it line by line, . . . the way opens up, becomes clear, and the structure holds firm under you despite the feeling that you are entering a cloud. When you reach the other side, you will know that the bridge of the poem has held you and led you into the poet's mind, experience, and emotion.
• For this to happen most effectively, you may want to read the poem aloud, and let its rhythm and the resonant music of its language enter your ear as the words penetrate your eye and the ideas and images reach your mind. This will vastly aid your comprehension of the poem. Read it aloud again. And again. Each time you read it, it will open itself up--make itself more accessible and vivid to you.
• Because a skillful poem often suggests rather than explains, there may be some enigmatic gaps, some silences, some breaks in logic, which you will fill in from your own imagination, your own set of kaleidoscopic impressions.
• A poem is as different from descriptive or expository prose as singing or whistling is from talking. You must come to poetry with a different set of expectations than you would with a sermon on the raising of Lazarus, or a lecture. . . . Where most prose gives us information or instruction, poetry offers reflection on something wonder-full, some event or phenomenon that has caused the poet to express wonder . . .
• A poem rarely attempts to tell the whole story. It's not like a speech with an introduction, four points, a summary, and a conclusion. ... It is more like a small fragment of experience viewed close up. It hints, suggests, touches, probes, without preaching or pushing too hard. Poems are packed with sounds, pictures--the doorways to the inner life of objects, experiences, relationships--the stuff of the extraordinary ordinary.
• As you enter a poem you will need to feel and see it as well as to listen to it and analyze it critically. . . . Poetry is not irrational, but it arises from the logic of the imagination and the senses rather than from the purely linear, rational kind of thought.
• Practice a kind of relaxed concentration. Take time. Breathe deeply. Flow with the lines of words, and bridge your way into each poem with your ears, and your skin, and your nose, and your eyes, and even your tongue. See the word pictures. Pretend your mind is a projection screen on which the poet is shining a series of images.