Formalized prayer is a very beautiful devotion and can be as simple or as complicated as you wish. 

Act of Contrition (a prayer for asking forgiveness)

O my God, I am heartily sorry for having offended You and I detest all my sins, because I dread the loss of heaven and the pains of hell, but most of all because they offend you, my God, who are all good and deserving of all my love. I firmly resolve, with the help of your grace, to confess my sins, to do penance and to amend my life.

Our Father (Lord’s Prayer)

Our Father, Who art in heaven, Hallowed be Thy Name; Thy kingdom come,
Thy will be done, on earth as it is in heaven.  Give us this day our daily bread,
and forgive us our trespasses, as we forgive those who trespass against us;
and lead us not into temptation,
but deliver us from evil. Amen. (the part after this point saying , “For thine is the kingdom and the power and the glory now and forever.” is actually from the Doxology in the Mass.  It is not a part of the Bible text. This was added during the 1500’s in the Protestant churches.) 
The Our Father is based on the passages of the Bible: Matthew 6:9-13 and Luke 11:2-4

Hail Mary

Hail Mary, full of grace. The Lord is with thee.  Blessed art thou amongst women and blessed is the fruit of thy womb, Jesus.  Holy Mary, Mother of God, pray of us sinners now and at the hour of our death. Amen.

Glory Be

Glory be to the Father, and to the Son and to the Holy Spirit.  As it was in the beginning, is now, and ever shall be, world without end. Amen.

Fatima Prayer

Oh my Jesus, forgive us our sins, save us from the fires of Hell, and lead all souls to Heaven, especially those most in need of thy mercy.

Sign of the Cross

(tap the forehead) In the name of the Father, (tap the stomach) and of the Son, (tap the left shoulder) and of the Holy (tap the right shoulder) Spirit. (fold hands in prayer) Amen.