@psyche1992,
First of all you have to:
Understand the poem. All poems have a literal meaning. Often, they also have a figurative meaning. You can try to analyze the poem yourself; but it's probably far easier to read what others have said about it. From published criticisms you can learn about things such as themes, symbolism and voice. It's also helpful to learn about the poet and what he or she was doing at the time the poem was written.
Memorize the poem. Most poems have a meter and rhyme scheme that make them easy to memorize.
Reformat the poem. Once you've learned all the lines of the poem, you'll want to abandon the habit of progressing line by line and instead put the phrases together in a more natural way. Learn the poem again without relying on the sing-song rhythm that helped you initially memorize it. It may help to write the poem down as if it were prose.