Break the poem down into parts such as stanzas or couplets. Memorize each part first, and then move on to the next. Memorize the parts in sequential order so you don't get confused. Ultimately, learning a little each time and then adding on to the parts you're confident with will be faster and less overwhelming than trying to memorize the whole thing at once.
Take note of the rhyme scheme, if there is one, which will help you group the poem by rhyming lines. For example, if you get stuck on a line that ends with "wall" you may remember that it is grouped with a line that ends with "all." This may jog your memory and help you recall the entire line.
Write the poem over and over. Copying the poem in your own hand forces you to engage the poem in a more direct way than simply reading it repetitively. Test yourself often by trying to write the parts you've memorized and then checking over the parts you've had trouble with and writing them over and over.
Listen to the poem. Either use a recording device and listen to the poem read in your own voice, or find an audio recording of the poem online. Hearing the poem over and over while you are concentrating on it will help you memorize it quickly.
Analyze the poem's meaning. If the poem has a narrative structure and tells a story, it may be easier to remember it by remembering the events in sequence. If the poem makes a series of observations about life and then comes to a conclusion, it will be easy to remember that the conclusion comes last. While you are committing the poem to your memory, keep thinking back to why the poem was written, what it means, and why the poet chose the particular sequence.