I always try to get my students to play around first with the syntax of each line, and to avoid the end of a line of poetry as a form of punctuation. Often the word order is dictated by a rhyme scheme being followed. And just because a line ends, that doesn't mean the thought ends. The last thing I would do would be to have students define words they are unfamiliar with. Putting the lines into sentences, with a more "logic" and contemporary word order, and an understanding of all the words, within the context of the poem, goes a long way in helping me to understand more difficult poetry.
I too have had much success with the SOAPS method. Lately though, my seniors have used the TPCASTT mnemonic to help my students wade through their poems.
1. Title. Just like with books and movies, titles often offer insight into the poem. However, quick to finished reading the poem, students often omit it.
2. Paraphrase. When students are able to take the poem's words and put them into their own vernacular, they often find the meaning less difficult to determine.
3. Connotation. Look beyond the literal meaning of the poem. Does the author employ any literary strategies?
4. Attitude. What is the subject of the poem and how does the author (or speaker) feel about it?
5. Shifts. Are there any transitions in the poem? These can include subject, tone, mood, or motif.
6. Title. My students don't always like this step. But we look at the title again. Since we've now read through the poem and determined what it's about and the attitude of the author, we re-examine the title to see what other insights it may provide for us.
7. Theme. Now that we know the subject and meaning of the poem, we determine what the author thinks about it by determining his or her opinion.
Three things that I've found useful for those who are struggling with meaning in poems are to attend to punctuation and meter, then (as already suggested) write a paraphrase of the poem. Punctuation: Attending to punctuation shows how the poet constructed their ideas. Where are the semicolons, which indicate closely related thoughts? Where are the periods, which indicate the end of one thought and the beginning of the next? Where are the commas, which indicate continuing thought? Do the line-ends have punctuation or are they enjambed (have no thought interrupting punctuation of any kind)? After analysing punctuation in this way, you can better answer: What are the poet's thoughts?
Meter: Meter gives the rhythm and therefore the emphases in the poem. The emphases in words lead to the emphases in expressed thoughts. To identify rhythm, start with what might be called the anchor words--the words that the rhythm is tied to because English pronunciation requires a specified syllabic accent. For instance, Constantinople might be such a word; anticipate is another. The first would fit only in iambs because it has a minor accent stress on -stan and a major stress on -o: kɒnstæn'tn oʊ''pəl (IPA). The second would fit only dactylic because accent stress is on the second syllable and is followed by two unstressed beats: an-tis-uh-peyt. Find the emphases in the rhythm portion of the meter and you have a clue to meaning.
Paraphrase: Write in your own prose words what each line or logically expressed group (e.g., lines not interrupted because of enjambment; lines interrupted by only a comma; etc) of lines means. You will be surprised at (1) how some Gordian Knots of meaning untangle themselves and (2) how many more words you need than the poet used!
I think the biggest strategy that certainly helps my students is by starting simple. Remember that often in poetry there are so many different meanings that even critics disagree about how to interpret poetry. Therefore, as long as you can support your particular view of a poem with reference to the text, that is absolutely fine. Obviously you can't go way out and argue that a poem about daffodils is actually about vampires, for example, but at the same time the richly symbolic nature of so many poems does open them to a variety of meanings.
You should also be aware of any words or phrases that appear again and again or are used in interesting ways. This should be an indication that they are important and linked to the meaning of the poem. I also like the idea given in #7 about imagining how words can be replaced by other words and how this would impact the poem.
I agree with all the answers already given, and I especially like the "SOAP" method.
I always tell my students that it's helpful to remember that every poem begins with a blank sheet of paper (or a blank computer screen). Therefore, every word and even every piece of punctuation in a poem is, in a sense, a choice. The choices may be conscious and deliberate, or they may be unconscious and the result of intuition, or they may be some combination of the two.
For these reasons, I always suggest that my students to try to imagine what words the poet might have used in place of the words that presently appear. Considering alternatives to the present phrasing of the poem will help you better appreciate the precise meanings and the subtle nuances of the words actually chosen. The beauty of and effectiveness of poetry, in particular, depend on the appropriateness of particular words, since in most poems there are fewer words to waste than in a novel. Try to imagine, then, how any particular words could be replaced with something else.
One traditional approach to poetry is to uncover the information behind the word SOAPS:
S: Speaker - Who is talking? What kind of person are they? Male or Female? Authoritative or submissive?
O: Occasion - What is the circumstance that has caused the need for this communication right now?
A: Audience - Who are they talking to?
P: Purpose - What is the speaker trying to achieve by sharing this information?
S: Style - Is this formal or informal? Does it rhyme? What are some of the literary devices at work? How is it structured? What is the tone?
If you can understand these elements of a poem, or at least try to figure them out, then you will be able to better discuss and prove you understand what you have read.
One very important thing to consider in any poem is the title. Many analyses ignore the title in favor of whatever metaphor they find in the body, but the title can contain as much or more meaning in itself. Consider Frost; his most famous poem, "Stopping by Woods on a Snowy Evening," contains much to discuss in the body, but the title gives it a basic meaning to draw from: the narrator is literally stopping to look at woods on a snowy evening, and his thoughts come from this contemplation. Frost's "The Road Not Taken" is similar, but without the poem the title is little more than a platitude; taken together, they give power to the concept of choice.
I always tell my students that they have to approach the poem with a prepared "script" of questions they can "ask" the poem. If they work through the script, they will likely be able to put together a workable understanding of the poem as a whole. Whenever possible, they should work with a copy of the poem which they can annotate on directly.
To start: They should always read the poem all the way through once just letting the words and ideas come into their mind. They will be able to know the subject and perhaps overall tone.
Next: Review the poem to determine who the speaker of the poem is and if there is a "dramatic situation." It is never safe to assume the speaker and the poet are one in the same, so ask yourself: "What kind of person/speaker is talking here?" A man in love? A woman scorned? An observer of nature? Then determine the "story" of the poem. I literally tell students to imagine trying to make a film of the poem so that they can see how they could portray each section. Is there a conversation? Is there action?
Once they establish those essentials, then they should re-read the poem to try and determine places to break the poem into smaller chunks. The actual structure (stanzas) can be a start, but sometimes there are smaller chunks within a stanza.
Once they have the poem in manageable parts I usually tell them to reveiw the END of the poem because most often that is where the meaning of the poem makes itself most clear. The poet is building to that point, so if they understand that, they can work backwards to see how all of the other chunks contribute to that overall thematic point.
Then students should reveiw the poem from the start, mentally paraphrasing as they go and making note of the literary devices, diction, and sound devices that the poem is employing. Usually, by the time they have read and re-read the poem a few times, they see these things more easily and can connect their meaning to the meaning of the work as a whole.
Below are two links which provide some of the same strategies I have noted above, but with different elaboration, which may help clarify the process even more.
In my opinion better understanding of poems depends on visualization of the reader. Trying to visualize images and setting (time and place) in a poem will help tou to understand it's meaning to a great degree. Of course there are many poems in which have many abstract words, phrases or even concepts that are very hard to visualize; so for the begining try to start with those poems that are filled with images. Starting with those sorts of poems will make your progress easier and better.