Instructions
Read through what you wish to memorize to familiarize yourself with it. Not many people can commit something to memory at one glance, but reading something is at the very least a good introduction. If you are a musician or singer, play or sing a song sight unseen. This is called sight-reading (or sight-singing, if you are a singer). Few people can sight-read perfectly, but that's not the object here. The object here is to introduce yourself to a piece so you know what to expect when you begin studying it in earnest.
Pay close attention to possible musical themes and phrases, even if what you are studying has seemingly little to do with music. Listen to the natural rhythm of the words and how musical phrases are structured. See if there is a rhyme scheme. This will all help improve your memory on the subject. This is why so many ancient stories and poems were told in song and as poetry. Before the advent of the written language, everything had to be memorized. It was these musical elements that allowed people to memorize and tell stories and spread news.
Focus on small sections. Before you attempt to memorize an entire song, story or poem, memorize one part of it. Read through it, find a logical stopping point such as the end of a musical phrase or stanza, and try to memorize that one section. Once you have memorized one section, move to another section. Memorize the entire work in this way. When you recite it, you will think of it as a series of short pieces that are easier to recall.