How do Catholics regard the Bible?

Catholics hold the Bible to be inerrant Word of God.  "The Church has always venerated the divine Scriptures as she venerates the body of the Lord." (Dei Verbum 21). The teaching authority of the Church interprets Sacred Scripture and Sacred Tradition to communicate the sacred truths to all generations; this is how Christ "opens our minds to understand the scriptures" (Luke 24:45).

This teaching office is not above the Word of God, but serves it, teaching only what has been handed on, listening to it devoutly, guarding it scrupulously and explaining it faithfully in accord with a divine commission and with the help of the Holy Spirit, it draws from this one deposit of faith everything which it presents for belief as divinely revealed. (Dei Verbum 10)

- The Didache Bible

How were the books of the Bible compiled?

The teaching authority of the Church, through its reflection on Sacred Tradition, discerned and established which writings were inspired by God and therefore worthy of inclusion in the Old and New Testaments. "The Sacred Scriptures contain the word of God and since they are inspired, really are the word of God" (Dei Verbum 24).

The canon of Sacred Scripture is not found in the text of the Bible itself, of course, but is part of the deposit of revealed truths entrusted to and handed on by the Church. Under the guidance of the Holy Spirit, the Church developed a list, or canon, of those books that were determined to be divinely inspired. Through Sacred Tradition, the Church knows the canon of inspired books with certainty. (Cf. CCC 120)

By the time of the Incarnation, the forty-six books that make up today's Old Testament canon had already been written and appeared in the Septuagint (a Greek translation made by Jewish scholars in the third or second century BC). The Apostles and the early Christians used this version, even quoting it in the New Testament.

Late in the first century after the Resurrection of Christ, some Jewish rabbis in Palestine decided to exclude several books from their Scriptures because they were composed or preserved primarily in Greek or Aramaic rather than Hebrew. Christians had already been using and continued to use the full Septuagint, and they came to classify the books excluded by Palestinian Jews deuterocanonical ("of the second canon") while those they shared in common are called protocanonical ("of the first canon"). (Cf. CCC 121-123,128)

Besides the New Testament books we recognize today, there were numerous other "gospels" of the life of Christ, letters purportedly written by Apostles and other figures, and apocalyptic narratives in circulation. Some were of spurious origin, and others were tainted by false teachings or "revelations." Many originated with the Gnostics, a 
heretical sect that claimed secret knowledge and visions in order to justify their beliefs. (Cf. CCC 120,126)

By the third century most theologians and Church leaders agreed on the essential composition of the canon. In Rome AD 382, Pope Damasus and the bishops established the canon of the Bible. The Pope then directed that the Bible be translated into Latin, the language of the people. This canon was subsequently endorsed by numerous local Christian councils and reaffirmed by the Ecumenical Council of Trent (1546) and the First Ecumenical Council of the Vatican (1870). (Cf. CCC 131-133)

- The Didache Bible