Who was the author? The writing of this Gospel account was brought about by the Holy Spirit through a man named Luke, who was a Gentile doctor and both a friend to and coworker of St. Paul (see the so-called "we" portions of Luke's second book, Acts-Acts 16:11, for example).
What is the book? The book is an orderly account of Jesus's life, death, and resurrection for the salvation of all people. St. Luke seems to assume his hearers' unfamiliarity with the land where these events took place, so the book may have been written for people in Antioch, Achaia, or Ephesus.
Where was it written? Bible scholars suggest that the book may have been written in Rome, although Achaia, Ephesus, and Caesarea are also given as possibilities.
When was it written? A usual date for the writing of St. Luke's account of the Holy Gospel is 59-63 A.D., or perhaps a bit later. Some early church writings imply the account was written after St. Paul's martyrdom.
Why? In a formal preface (Luke 1:1-4), St. Luke states his purpose for writing: that Theophilus, possibly his patron, and all people might know the certainty of what he and they have been taught.
How? More than any other Gospel account, St. Luke gives the full scope of Jesus's life, from birth to ascension, in an orderly, detailed fashion that is said to be "characterized by literary excellence, historical detail, and warm, sensitive understanding of Jesus and of those around him." More than the writers of the other Gospel accounts, St. Luke is said to emphasize how God's plan also includes Gentiles, the importance of prayer, how people react to the Good News with joy, the role of women, Jesus's interest in the poor, His concern for sinners, family, His role as the Son of Man, and the role of the Holy Spirit (although John's account I think has more on the Holy Spirit). I might also mention St. Luke's focus on the Temple and worship.
For further reading on the book of Luke:
- Lenski, R. C. H. The Interpretation of St. Luke's Gospel. Minneapolis, MN: Augsburg Publishing House, 1961. (First published in 1946, Lenski's commentary is out of date as scholarship goes, but his interpretations are nevertheless generally reliable. He mixes more technical matters with general interpretation, but most readers would probably find his commentary quite accessible.)
- Marshall, I. Howard. The Gospel of Luke: A Commentary on the Greek Text. Grand Rapids, MI: The Paternoster Press of William B. Eerdmans Publishing Company, 1978. (I have the 1992 reprint of this volume of the New International Greek Testament Commentary, and, while it is a little more higher-critical than I might like, Marshall is generally conservative in his final position and interpretation. The average lay reader may find the format used and the Greek content to be barriers to meaningful use, however.)