The best preparation I know of for this is to develop said art in the here and now. In my case, God blessed me in this by redeeming my pre-conversion addiction to Fantasy/SciFi novels. Somewhere along the line I switched from "suspension of disbelief" (an expression I find fascinating - does that imply that most of us see disbelief as normal?) to "letting the story tell its story in its own terms". I may disagree with those terms, I may even find those terms horrific, but I'll agree to understand the terms and background the story is based on, rather than insisting on shoehorning it into my own terms and background.
That attitude can be shifted to people. In listening to people you agree to hear what they're saying in terms of their own background, assumptions and goals rather than insisting on fitting their words into yours. You don't agree to find their viewpoint as valid, but you do agree to try to see what they're trying to say from their own perspective.
This isn't easy, and may require abilities that some people simply don't have(carrying multiple perspectives in your head at once and keeping them straight isn't something everyone can do). But for those of us that can acquire it, this is a remarkably useful skill, profitable in a multitude of different areas. I at times wonder if you see this reflected in the introduction to the Psalms:
for attaining wisdom and discipline;
for understanding words of insight;
for acquiring a disciplined and prudent life,
doing what is right and just and fair;
for giving prudence to the simple,
knowledge and discretion to the young --
let the wise listen and add to their learning
and let the discerning get guidance --
for understanding proverbs and parables,
the sayings and riddles of the wise. (Pr 1:2-6 NIV)
If nothing else, this skill is invaluable if you end up involved in any way with counselling.
I can't give step-by-step instructions on learning this (because I didn't learn it that way), but Rule 1 is that miscommunication is extraordinarily easy, and can't be cured by precision of speech (as valuable as that is). You have to learn to spot the small clues that tell you that what you're hearing isn't what the speaker is trying to say, and let that alert you to check for background, assumption, perspective or terminological differences between you and the speaker, or to just plain ask for correction. Other than that, ask God to teach you and dive in. You'll make plenty of mistakes, but you'll learn from them. Along the way, you'll also get a much clearer idea of where your own particular perspective comes from (how can you contrast your perspective and the speaker's if you don't know where you're coming from?). You'll get a feel for how ordinary people communicate (which is often quite different from how scholars communicate). You'll learn to combine precision of concept with the imprecise way people often use words. And you'll figure out that sometimes you'll just have to admit you don't know, and wait for what it takes to give you clarity.
And you'll be much better prepared to read across those historical distances and actualy have a stab at getting what the ancients would have gotten out of it(not to mention following what the writer was getting at).