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.