1. Read the poem/poems aloud.
Poetry revels in sounds. Thus, you need to hear it with your ears. Also, many poems are built on rhythmic patterns, and this rhythm will more likely come alive for you when you hear it. You may need to read the poem aloud a few times before you can get a feel for the rhythym. However, keep reading. Read like you are auditioning for a role in a play -- with poetic emphasis!
2. Clarify or define unclear words/ concepts.
Many people are discouraged by the word choice (diction) of poetry. My guess is that most people are wary of poetry because they fear they won't understand it. And, why do they think they won't understand it? Because they come across unfamiliar words. So, keep a dictionary handy. You will learn a few new words. Also, an author may make an illusion to another work, and if you haven't read it, you are lost. So, simply go and check the reference.
3. Try to discern the artistic features of a poem.
Here are some important features to look for:
-repetition: words/ phrases repeated (key words are usually repeated)
-patterns: rhyme patterns, sound patterns
-genre: what kind of poem is this? (Sonnet, Ode, Epic, Free Verse, etc.
4. Look into the historical background of the poem/poet.
Who was the author? What do we know about him/her?
When did they live?
What is the occasion for the poem?
Who was the poem written to/for?
What were the historical circumstances of the poem?
Why did the poet write this poem? Do they give a reason in the poem?
5. Meditate on metaphors.
What are the metaphors (A IS B) and similes (A IS LIKE B), and what is the point of comparison (How A is B, or is like B)?
Our lack of emotional benefit in regards to poetry comes at this point exactly -- we fail to sufficiently ponder the point of comparison.