Most poems are imitations of speech, that is, they are meant to be imagined as something someone says, or could say, in a given situation. That's why, "Who's the speaker?" is usually the first question asked about a poem. It's also a reason why reading the poem aloud is important. Try to identify the poem's situation. What is said is often conditioned by where it is said and by whom. Identifying the speaker and his/her place in the situation puts what s/he says into perspective.
Articulate for yourself what the title, subject and situation make you expect. Poets often use false leads and try to surprise you by doing "shocking" things, but defining expectations lets you be conscious of where you are when you begin.
Be willing to be surprised. Things often happen in poems that turn them around. A poem may suggest one thing at first, then persuade you to its opposite (or at least be a significant qualification or variation).
Find out what is implied by the traditions behind the poem. Verse forms and metrical patterns all have frames of reference, traditions in the way that they are usually used and for what reasons they are used.
Bother the reference librarians. Look up anything you don't understand: an unfamiliar word (or an ordinary word used in an unfamiliar way), a place, a person, a myth, an idea--anything the poem uses.
Take a poem on its own terms. Adjust to the poem; don't make the poem adjust to you. Be prepared to hear things you do not want to hear. Not all poems are about your ideas nor will they always present emotions you want to feel. Be tolerant and listen to the poem's ideas.
Argue. Discussion usually results in clarification and keeps you from being too dependent on personal biases and preoccupations which sometimes mislead even the best readers. Talking a poem over with someone else (especially someone very different) can expand the limits of a too-narrow perspective.
Assume there is a reason for everything, from the space between words to the period at the end of the line.