The basic premise of this line is that the findings of faith and reason are not at odds--only their methods are. Reason is objective--discovered in the outside world. Faith is subjective--discovered within. Faith is about the metaphysical world, that world of events, occurrences, and mysteries that by their very nature can never be proved objectively.
4 Cultural/Historical Relativism
Relativists hold that religious texts written centuries ago must be interpreted within the cultural and historical context of their times. The Bible and Koran were written when the scientific laws the 20th century takes for granted were nonexistent. The writers had to make their points in terms that people of the time would understand. For example, had the writer of the Genesis creation story been composing for a 20th century readership, he or she would have explained God's hand in the evolutionary process as opposed to the more magical creation story in the Bible. Likewise, had Talmudic authors had the sanitary conditions of today, laws for keeping kosher might have been much less stringent or possibly omitted altogether.
Though this approach will seem quite reasonable to rationalists, it is one of the more controversial approaches to reconciling faith and reason. Its critics complain that God's truths are not and cannot be relative to the time they are written. There is a moral absolute that supersedes cultural and historical contexts.
5 Religious Texts as Allegorical Moral Literature
Possibly the antithesis of literalist theories, this approach assumes that the Scriptures were written solely for the purpose of conveying a moral message. Much like Aesop's fables, these theological works are said to use myth, imagery, and symbolism to instruct readers how to lead a good life. They are not historical or factual documents, since all the events within were composed as literary tools.
Once again, this is an oft-criticized approach. If the Bible and Koran are simply books of myths with morals, then they are no different from any other moral literature--they are stripped of their sacred significance.
The challenge the pope has thrown down is a formidable one. Reconciling faith and reason is hard work. There are other ways to go about it, but these five should be enough to get you started, God willing.