There is always important to be aware of the multi-lingual/ethnic/cultural context of that region, during the entire 1th century. Likewise, there is always important to be aware of the fact that the Gospels were written a couple of years (decades) after the events described. No less, there is always important to be aware of the fact that we have no such a thing as an original text.
So when we do exegesis of Jesus's/Apostles' we should take into consideration first of all as many versions as we can of the text, in the language that WE are using when speaking. YES, I am aware this might sound funny, but it is the best way to start with. There is no perfect translation of the Bible, yet every effort to translate the text is shedding a new light from a new perspective on it. Secondly, if you can, do have a look on other translations, in different other languages - this is very helpful too.
Thirdly, there certainly are some words, concepts, ideas, that are very important to be analysed in the "original", if we know it, if we can be sure that Jesus or the Apostles were using that particular word in hebrew/aramaic/greek.
In your specific example, John 8:58, I would be interested to find out why is Jesus beginning his utterance with Ἀμὴν ἀμὴν λέγω ὑμῖν? In the western tradition (very broadly speaking), you would rather end a sentence by ἀμὴν. Why is Jesus using it as a beginning? How it came that we start using it as an ending, like a full stop? Why was this translated into English as "Verily, verily" or "Truly, truly" or even "I tell you for certain" (CEV) or "The fact is" (ERV)? Ἀμὴν is not a Greek word, it is obviously a transliteration of something. You see, this is a case where English translations are so diverse, they try to express the same idea, yet they appear to be missing something that perhaps we can find out by taking into consideration the language that was used when speaking.