No. 1320 and 1321, page 333 of the Catechism of the Catholic Church: The Celebration of the Christian Mystery; Libreria Editrice Vaticana: Urbi Et Orbi Communications:
The essential rite of Confirmation is anointing the forehead of the baptized with sacred chrism (in the East other sense-organs as well), together with the laying on of athe minister's hand and the words: "Accipe signaculum doni Spiritus Sancti" ("Be sealed with the Gift of the Holy Spirit") in the Roman Rite, or "The seal of the gift that is the Holy Spirit" in the Byzantine Rite.
When Confirmation is celebrated separately from Baptism, its connection with Baptism is expressed, among other ways, by the renewal of baptismal promises. The celebration of Confirmation during the Eucharist helps underline the unity of the sacraments of Christian initiation.
From the Baltimore Catechism No. 3; Benziger Brothers, Inc. and Tan Books and Publishers, Inc. Nos. 685 and 686, page 141; Nos. 677, 680, and 684 pages 140 and 141; and No. 697, page 144.
Q. What does the bishop say in anointing the person he confirms?
A. In anointing the person he confirms the bishop says: "I sign thee with teh chrism of salvation, in the name of the Father, and of the Son, and of the Holy Ghost."
Q. What is meant by anointing the forehead with chrism in the form of a cross?
A. By anointing the forehead with chrism in the form of a cross is meant that the Christian who is confirmed must openly profess and practice his faith, never be ashamed of it; and rather die than deny it.
Q. How does the bishop give Confirmation?
A. The bishop extends his hands over those who are to be confirmed, prays that they may receive the Holy Ghost, and anoints the forehead of each with holy chrism in the form of a cross to signify the descent of the Holy Ghost upon us and the special protection of God through the grace of Confirmation.
Q. What do the oil and balm in Holy Chrism signify?
A. In Holy Chrism, the oil signifies strength, and the balm signifies the freedom from corruption and the sweetness which virtue must give to our lives.
Q. For what are the holy oils used?
A. Holy Chrism is used at Baptism and for Confirmation as well as some sacred things, such as altars, chalices, church-bells, etc., which are usually blessed by a bishop.
Q. Are sponsors necessary in Confirmation?
A. Sponsors are necessary in Confirmation, and they must be of the same good character as those required at Baptism, for they take upon themselves the same duties and responsibilities. They also contract a spiritual relationship.