Excerpted from  Billy Graham's website:

How to Memorize Scripture

Do you doubt your ability to memorize these Bible verses? Maybe these tips will help:

Say it aloud
Say the verse aloud so that you can hear it as well as see it and think it. Do you ever find yourself thinking about a song you have recently heard? Or about something someone has said to you? The ear remembers! Use this built-in "memory chip" to help you memorize Scripture.

Say it the same way each time
Write the verse on a card and include a topic name, such as "Applying God's Word," along with the verse and the reference. Each time you say the verse, do so in this order:

1.       The Topic

2.       The Reference

3.       The Verse

4.       Repeat the Reference

Reciting these four elements the same way each time will help you to firmly fix the passage in your mind.

Say it one phrase at a time
If you find the verse "too big for one bite," memorize it a phrase at a time, adding each phrase in order till you have the whole verse. Even if you start with just three or four words, say the reference before and after the phrase.

Say it again and again
The real secret of Scripture memorization is review, review, review. Quote the verses often, asking God for deep understanding and seeking to apply each verse to your life.