One example of this is in the book of Revelation. In fact, I could probably go to any verse in the book of Revelation and demonstrate intertextual links because the book of Revelation is essentially entirely borrowed from various parts of the Old Testament (I have heard some claim that every single verse is a reference to some OT passage). But, relevant to this discussion is Revelation 6 where we are introduced to the seven seals. And the first four seals are accompanied by four horses.
When one studies the intertextual links, it quickly becomes apparent that John is utilizing the language of Zechariah to shape the meaning of this particular vision. In fact, the Greek wording that John uses to name the four horses is the same wording that is used in the LXX of Zechariah. There, in Zechariah 6:2, we see four horses - three of which are the same colors as the first three in Revelation 6 (white, red, and black; the fourth horse in Zechariah is "dappled" while in Revelation is it "pale." I am not yet sure what to make of this difference).
The point in all of this is that when John wrote his vision, he knew that his audience would immediately call to memory these four horses in the book of Zechariah. And the meaning behind those four horses in Zechariah would be transfused into the meaning of Revelation. Some have described this practice as "short hand," as a way to get the full meaning of a particular point without having to reinvent the wheel, in some senses.
Now, there are some who propose that the practice of intertextuality in the Bible depends greatly upon the "unity of scripture," that is, that the Bible, from Genesis to Revelation, is unified in theme, purpose, content, and even authorship (ie., the Holy Spirit). But as I have thought about this more, I am not so sure that this is even necessary. Yes, I believe that scripture is united in all of these things. I have a "high view" of scripture. But in order for a person to make an intertextual case, I do not believe that this idea of the Bible's unity must necessarily be foundational.
Simply put, when John, for example, wrotethe book of Revelation, he wrote to an audience that was steeped in the tradition of the Hebrew scriptures. They knew the Hebrew Bible better than they knew the back of their hands. Many people were illiterate in those days and thus they often memorized large portions of scripture instead of reading it. And their recall of Old Testament language was, no doubt, incredibly remarkable.
So when John wrote about four horses, for example, this would have immediately brought to mind Zechariah - especially since this is the only place in the OT that talks about four horses.
To use a contemporary analogy, it would be like a newspaper writer today placing in an article the words "We hold these truths to be self-evident, that all men are created equal." Most American readers would immediately know that he is intertextually referring to the Declaration of Independence. It is simply the cultural and historical millieu in which we exist. Thus, we are able to understand the language he is couching his article in.
So what's the point? I guess my point is that we must learn to read the Bible through the lenses of those to whom it was written. Thus, when we read the New Testament we must keep in mind the Old Testament. When we read the Prophets and Writings we must keep in mind the Torah, etc. This may be easier said than done, but if we are some how able to do it, I think we would be able to gain far greater insights and appreciation for the message and content of the Bible.