The hermeneutical circle is not an approach--it is descriptive of a problem or state rather than prescriptive of a methodology.
The Communication Problem
The hermeneutical circle is a model or illustration used to explain that communication is a fundamentally difficult thing, and follows three basic steps:
Your perspective directly affects your reading of a text.
The text directly affects your perspective.
Therefore, it is vicious circle--you can never come to an objective conclusion about a text, because your perspective will always be changing, and thus your reading will always be changing.
A fourth step is often tacked on as well:
There is no objective truth in the text; only what the text says (and does) to you. We must abandon the concept of a univocal meaning, or "what the text really says". Instead of searching for the meaning of a text, one can impart any meaning one likes.
To a certain extent, this problem matches our experience. This is evidenced by a simple game of whisper down the lane.
Even this site itself shows us that perspectives and interpretations abound. If you have been convinced (by scripture) that Jesus is Messiah, you will surely interpret the Old Testament with that in mind. Others on this site do not come from that background of interpretation (again, convinced by scripture), and will likely have a very different interpretation. This would be be similarly true for various Christian denominations, issues surrounding sacraments, or gender roles, etc. The very idea of "scripture interprets scripture" used within Christendom only amplifies this idea.
And doesn't this also seem to match the way it should work? After all, the Bible is no book to be read for entertainment or information, that we would read it and put it down unchanged. The whole concept of the hermeneutical circle is based on the idea that readers are changed by the text, and surely as a Christian I would want to confess that yes, if these are the words of God, and the spirit works in us as we read holy scripture, we should and even must be changed.
After all, we are talking about the sword of the spirit, not just a bunch of words. How about teaching, reproof, correction, and training in righteousness? Don't these things change us?
Even further, Christians must recognize the devastating effects of the fall. We talk about the noetic effects of sin (that is, its effect on our minds) and we even have God explicitly making communication difficult at the incident at Babel.
And yet, there are a couple of objections to this model as well. Where the problem, as stated, starts from the reader and works to ultimate lack of objectivity, the Biblical argument here must start at the object as foundation and work to the subject as application.
The glaring issue with this whole model is that it is missing a foundational component: God.
God is omniscient and immutable. He knows with perfect understanding, and does not change according to the interpretation of a text. He is the objective knower, and has no communication problem.
Furthermore, God does not sit alone in heaven, simply being omniscient. God is a talking God. As John's gospel famously starts "In the beginning was the Word, and the Word was with God, and the Word was God." Some modern translations even render this as "In the beginning God expressed himself" or "made himself known". The point is that, for John, God's self-revelation is tied up in his identity.
God condescends to make himself known in his creation (see, e.g., John 1 and Romans 1), in the giving of his Son (see, e.g., Hebrews 1), and, of course in scripture itself. If this is so, then unlike the conclusion drawn by the Hermeneutical Circle, the goal is not to generate new and novel interpretations, but to understand the mind of God. Likewise, if scripture is authoritative, we can also be sure that what we are reading is not left to the interpretation of the reader.
But a gap remains. God is the perfect objective communicator. His self expression is no way lacking in clarity. His word does not return to him void. And yet, man is not perfect. We do not understand as we ought. How do we join these two pieces together?
Role of the Spirit
God did not simply give us the Bible and leave. He intends to make himself known, and will see to it. God has provided for us the Holy Spirit--God Himself--to help us to understand. As we read and interpret Scripture, we do not do so in a vacuum by ourselves, but are guided by the Holy Spirit. Likewise, we further enhance our understanding by asking the Spirit for help, and do so with faith that he will provide.
So, suppose that we do read based on our presuppositions, and that our presuppositions do change based on our reading; is it a foregone conclusion that we are left in a hopeless sea of subjectivity? Or can we know truly, even if we cannot know omnisciently?
An alternative proposal that some authors have proposed is known as the Hermeneutical Spiral. This model presents a way of acknowledging that we do change based on our reading, but that our change is directional. That is, as we pray, and read, and study, and pray, and read, round and round, we do not necessarily just go in circles, but, by the Spirit’s guidance, we really do get closer and closer to the text.
This understanding has been sometimes described like an asymptote. That is, as an asymptote approaches a line closer and closer without ever quite reaching it, so too our knowledge grows and we get closer and closer to a full understanding of the Truth expressed by God himself, without ever have a complete knowledge and understanding of God.
While we only see dimly, we do see. While we only know in part, we do know.
For now we see in a mirror dimly, but then face to face. Now I know in part; then I shall know fully, even as I have been fully known.
(1 Corinthians 13:12 ESV)