Are today's Catholics encouraged to study the Bible at home? How do Catholics view personal scripture study? Are members of the congregation encouraged to do any studying at home?
The short answer is yes:


  The Church “forcefully and specifically exhorts all the Christian
  faithful... to learn ‘the surpassing knowledge of Jesus Christ,’ by
  frequent reading of the divine Scriptures. ‘Ignorance of the
  Scriptures is ignorance of Christ.’”


-- Catechism of the Catholic Church, paragraph 133

The Church offers some strategies and practices for getting more out of scripture as well. One of note is Lectio Divina, a pretty old approach in which you are encouraged to approach a passage like so:


Read it. A fairly obvious step. You read the selected passage.
Meditate. Ponder the Living Word, trusting the Holy Spirit to guide you.
Pray. Speak with God about the passage.
Contemplate. Sit in silent, loving attentiveness to the Word of God.