To memorize a poem, read it aloud to yourself. Examine the poem's structure, and note any unusual words. Then use an index card to cover all but the poem's first line. Repeat the line until you can recite it from memory, and move on to the second line. Continue reciting the poem from the start, adding extra lines each time. Once you can recite the whole poem, continue reciting it to get more comfortable with the words.
Reading the poem aloud is important as it helps you to recognize the poem's rhythm. It is easier to memorize poems that have strong meters and rhyme schemes. Start by learning poems written in this style, as opposed to free verse. Look for connections between stanzas to help your memory move from one section to another.
If the poem contains unfamiliar words, which happens often with older poems, look up the words' meanings. Knowing what the poem means makes it easier to remember. Also try to learn the poem's story; even if it is not a straightforward narrative, find out what the poem is about. If you do not understand what the poem is about, it is much harder to memorize.
Try to remove any distractions when you are memorizing; turn off your cellphone and laptop. Once you can recite the poem, practice in front of the mirror, or to family and friends, so that you can give your best delivery.