One may think, as I did in some ways, that memorizing a book of the Bible is a huge, gargantuan, massively difficult task. If one learns how to do it, breaking it down into steps, the hardest part becomes simply maintaining the discipline to review what one has learned, and make progress on top of that.
First, choose a translation. Then, start with the first verse. As mentioned previously, memorizing more of a chapter is really a two-step process: (1) memorize another verse, and (2) stitch that together/onto what one has already learned. It just takes some patience and persistence when one hits unexpected bumps along the way. With adding a couple more verses each day, on average, one will have memorized a chapter in a couple weeks.
Memorizing a book of the Bible is no more work each day than memorizing a chapter of the Bible. Yes, this applies to even when one has memorized more than a chapter. This is because an effective stitching process really only needs at most half a chapter for adding on another verse. While I recommend the 3x4 (3 times x 4 directions) reciting practice to get it down solid, it would be neither practical nor necessary to spend 10-15 minutes each of those dozen times reciting as much of the entire book as one has learned.
As one goes along through this extended venture, even if you don't make progress each day, continue to review and keep fresh what has been learned so far.
As one is making significant progress through having memorized multiple chapters of a book of the Bible, it is good to go back through and review the entirety of what one has learned. I would recommend doing this at least once a week, more often earlier on in the process, if possible. I find on average reciting a chapter takes about two minutes.
With 16 chapters, that would put Romans at about 32 minutes. Some chapters are longer than average, and the most efficiently I have ever made it through Romans was in 36 minutes, and that was moving at a rather fast, not-totally-expressive clip. When I'm not as fresh or need to review or check a lot of spots along the way, it can take much longer, such as 50 minutes.
At four chapters, Philippians takes about 8 minutes. Colossians might be a bit shorter than that.
At six chapters, Galatians and Ephesians were closer to 15 minutes each.