The only permissible authority for the reformed is God himself, any other authority comes from man and is necessarily corrupt and sinful, a result of mans idolatrous mind. The Reformed is a religion of revelation, not of reason.
For this reason historical events are of crucial importance as it is through such events that the revelation actually took place, the ultimate historic event is the coming and teaching of Jesus as this is the event that the old covenant pointed to and the event that the new covenant rests on. Jesus taught that the Hebrew Old Testament was the very word of God and that his Church would be built by the Apostles. The Apostles explicitly claim that their writings were the very word of God. From a very early date the Church accepted the authority of both the Old Testament and what was continually being codified as the New Testament.
This brings us to the second seat of authority, the Church. Individuals are prone to error and the extremities of sin, the Church has authority in establishing and maintaining what is correct Christian belief and practice, but such authority cannot replace or contradict the direct revelation of God to be found in the Bible, rather the Church has to interpret such authority and it ceases to be the Church when it ceases to be subject to such authority. The Reformed uphold the great ecumenical Church Councils, the great creeds (i.e. the Nicene Creed) and confessions (i.e. The Westminster Confession of Faith), the reformed also believe that the church should set forth its teaching in catechism's (i.e. the Heidelberg Catechism) that regulate what individual christians should believe. These documents do not establish what is the truth, they arise from God's revelations and are only authoritative to the extent that the original revelation was authoritative and that they accurately mirror this revelation. The Christian should seek to understand these teachings with reason being the servant of faith, not making reason itself an idol.
When the Bible is interpreted the Reformed view is that as the revealed word of God the Bible cannot contradict itself, it is therefore incorrect to accept that such contradictions exist and to pick what your favourite interpretation is, that is nothing more than letting loose the idol factory. The full Cannon of scripture must be examined and clearer passages of scripture should be used to interpret more seemingly obscure passages, any apparent differences being reconciled. This is the root of the love the Reformed have for systematic theology, There is a belief that the bible can be reconciled into a cogent and logical statement of belief. The success of this approach can be seen in the great and magisterial systematic theologies, such as Calvin's own "Institutes of the Christian Religion". It is the Church that has the authority to interpret scripture according to the historic "regula fidei" or rule of faith. Irenaeus summed up this rule of faith in around 180 AD:
"believing in one God, the Creator of heaven and earth, and all things therein, by means of Christ Jesus, the Son of God; who, because of His surpassing love towards His creation, condescended to be born of the virgin, He Himself uniting man through Himself to God, and having suffered under Pontius Pilate, and rising again, and having been received up in splendour, shall come in glory, the Savior of those who are saved, and the Judge of those who are judged, and sending into eternal fire those who transform the truth, and despise His Father and His advent."
While the Bible is central to the Reformed view of authority it is important that the Bible does not itself become an idol, in the New Testament the Old Testament is often quoted directly from the Septuagint, a popular Greek translation of the original Hebrew document. The Septuagint is much studied to this day and as a translation of the Hebrew it leaves much to be desired, but nowhere in the New Testament is any mention made of differing interpretations or any admonishment of such an imperfect translation. Translation is an important issue, any translations should be true to the original and the translators should be careful not to create a translation according to there own minds and inclinations, but we worship God, not the translation or even the original script. For this reason there may be a certain distrust of "popular" translations (especially paraphrase translations) but there is little support for the King James Only idolatry that is so common in the fundamentalist churches.
When the Reformation occurred one of the most striking issues is the problems that breaking with The Church of Rome entailed, The Church has great authority and a break was only justified because the Roman church had ceased to seek to act in accordance with the teaching of the Bible. In the same way that all scripture must be reconciled so the Church cannot diverge from the Bible, if it does it ceases to be a Church and becomes a system of idolatry. For that reason attempts were made to return to the early church and to act according to the teaching of the Church fathers. Much of the early Reformed writing was centered on proving the compliance of the Reformed with such teaching and the great historical Church Councils, from which Rome had long since departed.