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

Until I arrive, attend to the reading, exhortation, and teaching. 
1 Timothy 4:13

Sacred Scripture tells the story of how God's plan of salvation has unfolded throughout history.  "In the sacred books, the Father who is heaven meets his children with great love and speaks with them" (Dei Verbum 21).  Salvation history, however, is different from other kinds of history.  The Bible not only teaches the meaning of past events, but also reveals how those events affect every person's life in every age.  (Cf. CCC 101-104)

The Bible is inspired and inerrant.  God himself guided the Sacred Authors, who were enlightend by God the Holy Spirit to write what he wanted and nothing more, making it "not a written and mute word, but the Word which is incarnate and living" (Saint Bernard, S. Missus Est Hom.,4, 11: PL 183, 86).  Thus, God the Holy Spirit is principal author of Scripture; the human writers were the instruments through which he chose to reveal himself to his people. (Cf. CCC 105-108)

The Bible is also literature because it uses literary forms and techniques, such as stories, poems, dialogues, and figurative language to convey its meaning.  Insofar as these forms and historical, political, and cultural contexts in which they lived are not understood, the meaning of the Sacred Authors remains hidden.  These literary techniques were placed at the service of the religious purpose of the Bible. (Cf. CCC 109-119)

Sacred Scripture is not intended to be received either as a scientific treatise or as a mere historical record "but, as it truly is, the word of God"(1Thessalonians 2:13; cf. DV24).  It must be read in light of Sacred Tradition and the teachings of the Church in order to be properly understood.  This is why Scripture and Tradition form a single Deposit of Faith, which, guided by the Magisterium, which in turn is guided by the Holy Spirit, preserves and communicates Divine Revelation for all time. Cf. CCC 84-87)

- 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