Where does the Bible teach the Sacrament of Confirmation?
First, let us start with definitions. The Baltimore Catechism defines sacrament as an outward sign instituted by Christ to give grace. It defines Confirmation as "a Sacrament through which we receive the Holy Ghost to make us strong and perfect Christians and soldiers of Jesus Christ... We are called soldiers of Jesus Christ to indicate how we must resist the attacks of our spiritual enemies and secure our victory over them by following and obeying Our Lord... It is a sin to neglect Confirmation, especially in these evil days when faith and morals are exposed to so many and such violent temptations... By "these evil days" we mean the present age or century in which we are living, surrounded on all sides by unbelief, false doctrines, bad books, bad example and temptation in every form... The effects of Confirmation are an increase of sanctifying grace, the strengthening of our faith, and the gifts of the Holy Ghost."
In 2 Corinthians 2:21-22, St. Paul writes, "And it is God who establishes us with you in Christ, and has anointed us, and who has also put his seal on us and given us his Spirit in our hearts as a guarantee."
The Greek word for "establishes" is bebaiōn. This word is defined by Thayer's Lexicon as "to confirm." In St. Jerome's Latin Vulgate, he translated it as confirmat, where we get the English word for Confirm. It is God who confirms us and anoints us through putting His seal on us and giving us the Holy Spirit.
In Acts 8:14-18, we read, "Now when the apostles at Jerusalem heard that Samaria had received the word of God, they sent to them Peter and John, who came down and prayed for them that they might receive the Holy Spirit, for he had not yet fallen on any of them, but they had only been baptized in the name of the Lord Jesus. Then they laid their hands on them and they received the Holy Spirit... Simon saw that the Spirit was given through the laying on of the apostles' hands."
This passage is very specific about this great Sacrament, which one could argue was initiated at Pentecost in Acts 2 when the Holy Spirit descended upon the Apostles in the upper room, equipping them to boldly proclaim the Gospel. Here in Acts 8, we see that the Apostles encounter Samaritan converts who had "only been baptized," however the Holy Spirit "had not yet fallen on any of them." So they laid hands on them that they "might receive the Holy Spirit." This is explicitly teaching us the Sacrament of Confirmation as something distinct from Baptism, and one which equips us with the Holy Spirit.
We encounter a similar episode in Acts 19:1-6. "And it happened that while Apollos was at Corinth, Paul passed through the inland country and came to Ephesus. There he found some disciples. And he said to them, “Did you receive the Holy Spirit when you believed?” And they said, “No, we have not even heard that there is a Holy Spirit.” And he said, “Into what then were you baptized?” They said, “Into John's baptism.” And Paul said, “John baptized with the baptism of repentance, telling the people to believe in the one who was to come after him, that is, Jesus.” On hearing this, they were baptized in the name of the Lord Jesus. And when Paul had laid his hands on them, the Holy Spirit came on them."
Again, we see believers who undergo Baptism, and then afterwards, hands are laid on them (a priestly function) so that the Holy Spirit could come upon them.
St. Theophilus of Antioch, 181 AD: Are you unwilling to be anointed with the oil of God? It is on this account that we are called Christians: because we are anointed with the oil of God.
Tertullian, 203 AD: So also with us, the unction runs on the body and profits us spiritually, in the same way that baptism itself is a corporal act by which we are plunged in water, while its effect is spiritual, in that we are freed from sins. After this, the hand is imposed for a blessing, invoking and inviting the Holy Spirit.
St. Hippolytus, 215 AD: Then, pouring the consecrated oil into his hand and imposing it on the head of the baptized, he shall say, ‘I anoint you with holy oil in the Lord, the Father Almighty, and Christ Jesus and the Holy Spirit.’ Signing them on the forehead, he shall kiss them and say, ‘The Lord be with you.’ He that has been signed shall say, ‘And with your spirit.’ Thus shall he do to each.
St. Cyprian, 253 AD: It is necessary for him that has been baptized also to be anointed, so that by his having received chrism, that is, the anointing, he can be the anointed of God and have in him the grace of Christ.
Later in the same writing, Cyprian comments on the above passage from Acts 8: Since, then, they had already received a legitimate and ecclesiastical baptism, it was not necessary to baptize them again. Rather, that only which was lacking was done by Peter and John. The prayer having been made over them and hands having been imposed upon them, the Holy Spirit was invoked and was poured out upon them. This is even now the practice among us, so that those who are baptized in the Church then are brought to the prelates of the Church; through our prayer and the imposition of hands, they receive the Holy Spirit and are perfected with the seal of the Lord.
St. Serapion, 350 AD: So that those baptized and anointed in the tracing with it of the sign of the saving cross of the only-begotten... as if reborn and renewed through the bath of regeneration, may be made participants in the gift of the Holy Spirit and, confirmed by this seal, may remain firm and immovable, unharmed and inviolate.
St. Pacian, 383 AD: If, then, the power of both baptism and confirmation, greater by far than charisms, is passed on to the bishops, so too is the right of binding and loosing.