Hello!
I too have had issues with the concept of biblical meditation and after reading quite a bit on the subject, I think it is an easy thing to over complicate. I'm one who over-analyzes and researches the death out of a topic and so I found meditation to be a bit frustrating as I know it is of great importance. I'm not an expert on the subject by any means, but I have found that meditation and the "stirring up of affections" happens organically when I reach a passage that catches my eye. Sometimes I need to read for awhile before I reach such a passage, but when I do it stands out and from there I thoroughly think about it. And sometimes I do the same on passages that I need such as some of God's promises. It doesn't have to "pop-out", but that is how I typically choose a passage to meditate on. Next, I think about its implications in all of the applicable areas of my life. I mean
every implication it has on life, in history, me, family, etc. I basically think on the passage until my knowledge of its contents becomes understanding, and it is when knowledge becomes understanding that the passage becomes soaked into my being. This then leads to prayer and worship as the reality of the passage always produces a response. So I pray, focus solely on the text, read until my heart is aligned or in focus, focus on the portion of a text prayerfully, and contemplate its meaning until I really get it. I typically end up praying the passage in some shape or form.
A loose Example: Psalm 23, "The Lord is my Shepard". While I can know the Lord is my Shepard I must understand how he is my Shepard. So I think about how he guides, watches, cares etc. over me. Of course the entire context of psalm 23 is important to be aware of. I tend to avoid isolated verses unless they are straight forward. When I understand that the Lord is my Shepard, I then pray the passage, "Father, thank you for being my Shepard, for protecting me and giving me rest where the water never dries up..." and so on.
I found meditation difficult, because I'm not really an emotional person and so the best way for me to identify meditation was to recognize the difference between knowing the passage and understanding it. There is a big difference in knowledge and understanding and while we all know that, we must understand it. It also applies to theology, I've found, but that is a different topic. Meditation is also difficult in our world of distractions, and put that with my ADD and it became really frustrating. Ultimately, I was left with waking up a couple of hours earlier where there was nothing else going on that could possibly distract me. For example I have to be at work at 6:00 AM (five minute drive) so I wake up at 4. On weekends my daughter and wife sleep until about 8:00am, so I wake up at 5:00am. I've found it really helps distractions and morning meetings with God are biblical!
Maybe this will help? I'm not sure.I do like the excerpt Matthew provided, though! I apologize for errors in my writing if there are any.
-N.C.