"You have not chosen me. I have chosen you. Go and bear fruit that will last." (John 15:16)
Go here for a website run by Fr. Roger Smith of one Sacred Heart Church in Morton WA. This is the best source I've found for all things regarding devotion to the Sacred Heart of Jesus, how it is accomplished and including its history.
Briefly, this devotion was given to the world through one St. Margaret Mary Alocoque in 17th century France. This devotion effectively squashed the heresy of Jansenism and greatly helped Christians to come to know more of the great love God has for us. Jesus revealed to us, through his humble servant St. Margaret Mary that His heart veritably burns for love of us.
In His great generosity, which we don't deserve...Jesus has granted mankind twelve promises to those who faithfully practice this devotion:
The Twelve Promises of Devotion to the Sacred Heart of Jesus
1. I will give them all the graces necessary for their state of life.
2. I will give peace in their families.
3. I will console them in all their troubles.
4. They shall find in My Heart an assured refuge during life and especially at the hour of death.
5. I will pour abundant blessings on all their undertakings.
6. Sinners shall find in My Heart the source and infinite ocean of mercy.
7. Tepid souls shall become fervent.
8. Fervent souls shall speedily rise to great perfection.
9. I will bless the homes in which the image of My Sacred Heart shall be exposed and honoured.
10. I will give to priests the power to touch the most hardened hearts.
11. Those who propagate this devotion shall have their name written in My Heart, and it shall never be effaced.
12. The all-powerful love of My Heart will grant to all those who shall receive Communion on the First Friday of nine consecutive months the grace of final repentance; they shall not die under My displeasure, nor without receiving their Sacraments; My Heart shall be their assured refuge at that last hour.
In our home we have an 8 x 10 print of the Sacred Heart over our fireplace mantle in the living room. In our prayer room (a renovated second floor porch) we have a larger statue of Jesus with His most Sacred Heart situated between statues of Mary and Joseph. Our family is also assisting Mass on First Fridays. Part of our family spiritual practices is reading books together on the lives of the saints. One of the best was the life of St. Margaret Mary, available here. My husband and I enjoy the books just as much as the kids do - St. Catherine of Siena is especially good too. As a family we often dedicate one decade of our rosary to reparation to the Sacred Heart. I also encourage my children to offer other communions, sacrifices and such in reparation for sins of indifference and blasphemy against the Sacred Heart. These are offered simply as examples of various ways to practice this great devotion.
Please feel free to share different ways in which you practice this devotion in the combox.