The teachings of the Catholic Church on Mary and the communion of saints might be summarized in the following points:
Read the Catechism of the Catholic Church, #484-507, 946-962
Read parishioner and theologian Bob O'Gorman's chapter on Mary in The Idiot's Guide to Catholicism
Pray the Rosary! Read about how to pray the rosary here.
Here is another good place to read about the rosary: here.
Weekly Meditation: Memorize the Hail Mary
The Rosary offers a lovely intersection of vocal, meditative, and contemplative prayer, and it centers chiefly on the prayer known as the Hail Mary:
Hail Mary, full of grace, the Lord is with thee.
Blessed art thou among women, and blessed is the fruit of thy womb, Jesus.
Holy Mary, mother of God, pray for us sinners,
now and at the hour of our death. Amen.
One of the most well-known prayers in Catholic tradition, the Hail Mary is made up of two parts. The first half, taken from two verses in Luke's Gospel (Luke 1:28, Luke 1:42), express our gratitude and wonder at God for Mary's role in salvation history: Hail Mary, full of grace, the Lord is with thee. Blessed art thou among women, and blessed is the fruit of thy womb, Jesus. The second half, which gained widespread usage in the late middle ages, ask for Mary's ongoing participation in our salvation: Holy Mary, mother of God, pray for us sinners, now and at the hour of our death.
This prayer serves as the basis for the rosary -- through its repetition, we seek to enter more deeply into the mysteries of Christ's life and mission. The Hail Mary is especially useful when we don't know what to pray or when we feel alone, for in Mary we are always assured of God's maternal and life-giving love. Take a few minutes to pray this prayer. Feel its rhythm, its cadence, its warmth. Try to memorize it in small bits, perhaps saying its phrases throughout the day. Let it draw you toward the mystery of God's redemption of the world, as we all await amidst great labor pains the birth of Christ in our lives.