There’s plenty more to be said about context, but the concept of Book->Chapter->Verse is sufficient to get a new reader thinking about the topic. The next thing I’d want to mention is literary genres.
One of the major problems I see with people reading the Bible is that they want to read it all as legal code. Or, at least, they read it looking for commands that they are supposed to follow. That may be especially true for those of us from the Church of Christ, but I suspect it occurs in other groups as well. People are told, “This book contains God’s will for you,” so many think that means that the Bible is full of rules they are supposed to follow. Those people tend to find the epistles especially attractive, because they contain more instructions than most other books in the Bible.
Once people see that most of the Bible ISN’T merely a list of laws, they can begin to learn how to read different genres. They can learn to read narrative and find applicable teachings for them. They can differentiate between the hyperbole of proverbial statements and the symbolism of visionary writing. Thinking about genres helps us see what the gospels are saying to us today and help us read the letters as the situation-based documents they are.
Just as we read the sports page differently than we read the obituaries, so we must learn to read Revelation differently than we read Ecclesiastes.
One word… I don’t emphasize “rightly dividing the Word” as much as many in my fellowship do. The fact that we aren’t under the regulations found in the Torah has led many to basically disregard the whole Old Testament. (I’ve told the horror story of being in a meeting where a preacher scolded another man for quoting from Psalms; “My Bible says that’s been nailed to the cross!” All these years later, I still marvel at such ignorance in one who had been a Christian so long.) When we stop trying to parse out laws from every line of Scripture, such distinctions lose their importance.
I know that a lot of older Christians also need to be introduced to the concept of literary genres. Let’s give new readers a head start. Teach them early that within the sacred anthology that is Scripture, there are different types of writings that need to be read in different ways.