First, I believe the best way to approach John is by contextualizing his gospel in the first century when it was written. Most modern readers encounter John as modern readers; that is to say, we read it in light of the social, religious, linguistic and intellectual context of the early twenty-first century, nearly two thousand years after John wrote. We tend to read John while intellectually engaged with the theological and moral issues of our modern age. In one sense this is completely natural; if John could not speak to the concerns of twenty-first century readers, no one would read him. On the other hand, this can cause distortion in John's original message. For example, it is very difficult for modern Christians to read John without Nicene concepts of the Trinity impinging on their reading in one way or another, even though these ideas did not fully emerge until nearly three centuries after John wrote his gospel. Likewise, the theological debates of the Reformation, and the ways the Reformers and Counter-Reformers read John, form a fundamental, though often unrecognized theological context for many modern Western readers—though not for Greek Orthodox readers.
John, on the other hand, wrote while intellectually engaged with the theological, political and moral issues and assumptions of the overlapping Jewish and Hellenistic worlds of two thousand years ago. The best way to understand John is to understand his original historical context. Unfortunately, most modern readers are unfamiliar with John's ancient language and context, which is why commentaries can be so useful, aiding the modern reader by facilitating our understanding of John's ancient world of thought. Much of what I will do here is to try to approach John, as best we can, through the intellectual lenses of first century readers. My primary question will always be: "How would a first century reader have understood John?"
Second, when John originally wrote his gospel there was no New Testament. Most of John's original readers had no access to any other gospel, nor to the letters of Paul. John must have intended his gospel to stand alone, because he had no other option at the time. He did not expect what he wrote to be supplemented by other Christian writings, nor to be compared or harmonized with the Synoptic Gospels, which were not available to John. Most modern readers read John in conjunction with the Synoptic Gospels, trying to make sense of all four gospels simultaneously, to get as complete an understanding of the life and teachings of Jesus as possible. In many ways this approach can be very useful, but it should not be our only approach.
Some of John's readers were undoubtedly Christian neophytes. Others had probably been Christians for years. Most of what these original readers knew about Jesus, however, came from oral teachings, along the lines of the teaching practices described in Acts and the letters of Paul. John would have originally been understood in light of a body of oral teaching about Jesus known to his original readers, but which is now lost, at least in part. Indeed, many of John's readers might have heard different—though not necessarily conflicting—oral teachings of Jesus. Thus, paradoxically, we can't ignore the rest of the New Testament, since it—along with the Old Testament and other contemporary Jewish writings—reflects at least part of the oral knowledge about Jesus of John's first readers, and thus forms the most important part of the ancient historical context of John described above. However, to understand John as he intended to be understood, and as his first readers would have understood him, we must let John's gospel stand alone. We must first make sense of John as an independent witness to Christ before we compare and contrast him with the Synoptic Gospels, or Paul's teachings about Jesus.
Another assumption I will be making is that John intended his Gospel to be understood. Unfortunately, when reading ancient sacred texts this is not necessarily an obvious assumption. Some ancient texts were intentionally incomprehensible, trying to pass off incoherence as profundity. John is indeed sometimes enigmatic, but I don't believe that John is ever intentionally obscure. He wanted to be understood, because it was by understanding his message that his readers would come unto Christ (Jn 20.31). Unfortunately I believe that many modern scholars of John often tend to look beyond the mark in this regard. Despite the manifest brilliance and intriguing insights of many commentaries, it is highly unlikely that John intended his message to be understood only after reading a thousand pages of commentary. The main reason modern commentaries are necessary is that, after two thousand years we no longer share the same cultural and religious context that John's original audience could more or less take for granted. Commentaries permit us to enter the conceptual world of John's first readers and read John through their eyes. However, many commentaries spend a great deal of time arguing with other modern scholars or quibbling over minutia of Greek grammar. While this certainly has its place in modern scholarship, it can sometimes distract from getting at the essential concept of John's message. As we read through John we need to not get too distracted, and constantly remind ourselves to focus on the question: what is John's main point?