Old-Earth Creationism (OEC) relies on the understanding that God is the author of both the Bible and all that is created, known as Dual Revelation. Dual Revelation has two components - Special Revelation and General Revelation. Special Revelation is God revealing Himself to man throughout history, as He did to His chosen people, the Israelites, and through His written Word, the Bible. Special revelation, when understood by man, leads to salvation through Jesus Christ.
General Revelation is how God reveals Himself to all mankind through His created world. God's Word tells us that He has revealed Himself to us through His creation. David, in Psalm 19:1-4, declares, “The heavens declare the glory of God; the skies proclaim the work of His hands. Day after day they pour forth speech; night after night they display knowledge. There is no speech or language where their voice is not heard. Their voice goes out into all the earth, their words to the ends of the world.” Paul tells us in Romans 1:20 that "man is without excuse" - "For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse."
While accepting this reality, it is logical to follow that what we study in His Word will not conflict with what we study in His World. In essence, our theology should not conflict with our science. The reformers also understood this concept, as evidenced in Article II of the Belgic Confession of 1561:
We know God by two means:
First, by the creation, preservation, and government of the universe, since that universe is before our eyes like a beautiful book in which all creatures, great and small, are as letters to make us ponder the invisible things of God: God’s eternal power and divinity, as the apostle Paul says in Romans 1:20 (For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse.). All these things are enough to convict humans and to leave them without excuse.
Second, God makes himself known to us more clearly by his holy and divine Word, as much as we need in this life, for God’s glory and for our salvation.
Theologically, OEC interprets the days in Genesis One as long periods of time. The original Hebrew word which is translated as day in Genesis One is yom. Although our English Bibles translate yom as day in Genesis One, it has many different meanings. We need to understand that the ancient Hebrew language only had about 8,000 words, compared to modern Hewbrew which had over 100,000 words. Modern English has about 170,000 words (between 600,000 and over one million if you count word derivatives and old-fashioned words not in use anymore). Click here for an article by Greg Nyman of Old Earth Ministries on yom.
Scientifically, OEC accepts modern science's age for the Earth, 4.54 billion years old, and the Universe, 13.8 billion years old. OEC differs from Evolutionary Creationism, or Theistic Evolution, in that those adhering to OEC do not accept evolution. There are a number of different views of Creation that accept an old age for the Earth and Universe. Click on the names of the two more prominent views for OEC to are the Day-Age and Gap views. For a discussion on the differing views of OEC, please read this article