Read the poem several times, and don't worry if it doesn't "make sense" right away. It is important not to put pressure on yourself to figure out the poem the first time. During this first reading, it can help to read the poem out loud and simply enjoy the sound of the words and the music of the phrases.
Circle or underline words or phrases that jump out at you. Again, don't worry about fully understanding everything. Simply mark whatever strikes you as unusual, puzzling, surprising, funny or moving. Sometimes you will see a word you don't know, or which is used in a way you haven't seen before. Sometimes you will see unusual syntax, such as an adjective coming after a noun instead of before. And sometimes you will see a historical or literary reference that bears further investigation.
Go back through what you have marked and look for patterns. At this point, focus on language rather than meaning. Look for things like repeated sounds and rhyming patterns. Is there a connection between the images used? Is the speech formal or conversational? Look up any words you don't know in the dictionary, as well as any historical or literary references. Finally, take any phrase you found difficult or hard to understand and attempt to paraphrase it.
Now turn your attention toward the speaker. Who is he? Can you tell if he is from a particular region? Is he educated or not? Is he an observer or a participant in the story? Focus on the emotional tone of the poem. Is it one of sadness, regret, anger, joy? Why is the speaker telling this particular story? Is there something he is leaving out?
Finally, examine the structure of the poem. Most poems have several turning points that involve a shift in emotion, a jump in time or a change in focus. Sometimes, unusual language or syntax like the kind you noted in Step 1 is an indication of a shift. Based on these shifts, what do you think the intent or theme of the poem is?