Question:
How do we as non-Greek (or Hebrew) literate Christians know which translation of the Bible is the most accurate. There are so many to choose from.

Answer:
There are two methods used in translating the Scriptures: Complete Equivalence and Dynamic Equivalence. Complete Equivalence has been used from the very first and is most accurate. Dynamic Equivalence came in about the middle of this century and is not to be trusted. In Complete Equivalence the effort is made to translate every word into a good flow of English. In Dynamic Equivalence, as I understand it, the effort is to produce the closest equivalent to the original message. What happens here is that many of the words, such as conjunctions, that our God gave us in the Scriptures when He inspired their writing are not translated; they are simply dropped. And sometimes, the meanings of words are changed. Often, too, the emphasis God gave in certain passages is lost as is the coordination/subordination of certain passages.

Now to answer the question. I think that unless we carefully compare translations in our study, we will likely not notice these losses. And these are serious losses. Also, I don’t think we should be seeking “an easier translation” to read. Even though we may sometimes find “easier reading” it will be at the expense of losing some of God’s truth. It isn’t worth it. The study of God’s Word is time-consuming, hard work. But this is well worth the time and hard work, for it has its present great benefits and eternal ones as well.
Having said this, I realize it is still not enough, for years of study are involved in this whole process. I can only further give a partial list of what I believe are the best translations and my own recommendations.
The New International Version, the New English Bible, The Jerusalem Bible and Today’s English Version (Good News For Modern Man) are four twentieth century versions using Dynamic Equivalence. They are not trustworthy but can profitably be used only in selected passages and for comparison.
John Nelson Darby’s New Translation, the King James Translation, The New American Standard Bible and the New King James Translation are four translations using Complete Equivalence. These are trustworthy. We can rely on them. There is no serious loss of God’s truth in them.
All my life I have used the King James and J. N. Darby. I consider JND to be the most faithful and accurate translation available and the best for study. And I use the King James along with it. I would recommend the New King James for those who have a problem with the old. And really try hard, don’t give up, in using JND; for those who persevere will have much benefit.
Finally, remember this above all. It is the Holy Spirit who teaches us. (There is not greater learning because of easy translations, as many think.) And we MUST come to the Lord in our reading and studies with subdued hearts and chastened spirits. He will teach those who are spiritually ready to learn.