Read and reread the poem in question. Whether it is one that you are familiar with, or one that you are approaching for the first time, repetition will help you find the nuances that reading once will not.
Look for rhythm in the piece as you read it out loud or have someone else read it to you. If you are able to hear the author read the poem that would be the best bet, but aloud to yourself is fine.
Search the poem for an overall meaning or sense of purpose. Most poetry will use symbols to convey a point without stating the fact plainly. Pay close attention to the way the poem makes you feel, and make note of these feelings as you read.
Identify the speaker when you interpret poetry. This will help you hone your ideas and focus your thought on the speaker and their main point. The speaker is not always the actual person writing the poem, as many poets will create a character for a certain piece.
Define all of the words that seem to have a significant meaning, and pay close attention to words that can have more than one meaning. These key words are a good place to start to interpret poetry.
Use your personal feelings and judgments about the piece to come up with the over all theme, and verify if you agree with the speaker or if you can sympathize with their situation. Interpretation is always subjective. Different people can read different things into a given piece.
Analyze your findings and choose specific images and lines from the poem to justify your point of view. Most everyone can agree on a major theme of a poem, but there will always be people who will argue any point.