I'm currently working on memorizing Philippians in its entirety. A method I've found helpful for memorizing longer sections of Scripture is to put the verses on 3x5 cards.
The 3x5 cards are easy to carry with me on the go so I can review the verses while on a lunch break at the park, sitting at a stoplight, or exercising.
I've experimented with both writing out the verses by hand (my handwriting is reasonably legible) and printing the passage on a sheet of paper and then taping it to the card (cheaper than buying printable 3x5 cards). I find the printing method works out well. There's even a Microsoft Word template available to make printing a bit easier.
If you'd like to get started with memorizing Scripture you may want to give this method a try. I've also listed a few Scripture memory resources here.