The Glorious Mysteries are then prayed on Saturday and Sunday. Asking the Holy Spirit to enlighten you during the readings at daily Mass will also help immensely. It is also okay to meditate on the meaning of the words of the prayers as you pray them, or even to meditate on the person for whom you are offering the Rosary. Some people offer particular intentions before each decade. You can ask God to grand you a favor, heal a sick person, or convert a sinner.
Intentions are as varied as the people who pray.
Ask for big and small gifts. In this sense, the Rosary is an exchange of gifts between friends. It is widely known that Our Lady answers seemingly impossible intentions to those who are first beginning to pray the Rosary. This is her way of drawing you closer to Her and to Jesus. She'll often surprise you.