FK, in Orthodoxy, Baptism is always followed by Chrismation so the sacraments should be looked at together. Here's what the GOA website says:
"BAPTISM
The Sacrament of Baptism incorporates us into the Church, the Body of Christ, and is our introduction to the life of the Holy Trinity. Water is a natural symbol of cleansing and newness of life. Through the three-fold immersion in the waters of Baptism in the Name of the Holy Trinity, one dies to the old ways of sin and is born to a new life in Christ. Baptism is one's public identification with Christ Death and victorious Resurrection. Following the custom of the early Church, Orthodoxy encourages the baptism of infants. The Church believes that the Sacrament is bearing witness to the action of God who chooses a child to be an important member of His people. From the day of their baptism, children are expected to mature in the life of the Spirit, through their family and the Church. The Baptism of adults is practiced when there was no previous baptism in the name of the Holy Trinity.
CHRISMATION
The Sacrament of Chrismation (Confirmation) immediately follows baptism and is never delayed until a later age. As the ministry of Christ was enlivened by the Spirit, and the preaching of the Apostles strengthened by the Spirit, so is the life of each Orthodox Christian sanctified by the Holy Spirit. Chrismation, which is often referred to as one's personal Pentecost, is the Sacrament which imparts the Spirit in a special way.
In the Sacrament of Chrismation, the priest anoints the various parts of the body of the newly-baptized with Holy Oil saying: "The seal of the gifts of the Holy Spirit." The Holy Oil, which is blessed by the bishop, is a sign of consecration and strength. The Sacrament emphasizes the truths that not only is each person a valuable member of the Church, but also each one is blessed by the Spirit with certain gifts and talents. The anointing also reminds us that our bodies are valuable and are involved in the process of salvation.
The Sacraments of initiation always are concluded with the distribution of Holy Communion to the newly-baptized. Ideally, this takes place within the celebration of the Divine Liturgy. This practice reveals that Orthodoxy views children from their infancy as important members of the Church. There is never time when the young are not part of God's people."
This is different from the Latin rite, but consistent with the various Eastern rites of the Catholic church.
In the Latin rite, confirmation is done at the age of reason; it is consonant with the meaning of the confirmant as becoming a soldier for Christ, capable, for example, to read and understand the scripture.
In the East, both Catholic Eastern Churches and the Orthodox Church, the meaning of chrysmation is the same, but the age is not considered a factor. These are not differences in doctrine, as in either case Christ supplies the soldierly strength on His own schedule.
The difference with the Orthodox is in the understanding of baptism. The Catholic belief is that it remits both the original sin and any personal sin up to the point of baptism, so that a new person, free from the sin of Adam, is born. When an infant is baptized, there is no personal sin, but there is original sin, and that is remitted. In addition, baptism effects the membership in the Church just like the Orthodox say. The difference regarding the original sin is not really a difference in the sacrament of baptism, but rather in the concept of original sin itself. Both agree that concupiscence -- propensity to sin -- is not removed by baptism.
Both also agree that the faith and the will to be baptised are necessary if an adult (or a child past the age of reason, as early as around 7 years of age) gets baptised; when an infant is baptised, the faith and the will of at least one parent is sufficient. The sponsors then take the responsibility to foster the infant in faith.
Of course, any baptism by water in the name of the Father, the Son, and the Holy Ghost is valid in or out of any church. E.g. in an emergency a non-Christian may perform a valid baptism, if he uses water, the Trinitarian formula, and intends the procedure to have the Christian meaning even in absence of his personal understanding of that meaning. Certainly Trinitarian Protestant baptism is valid.
Thank you both very much for your answers on baptism and Chrismation. My first question to you, Kolo, was going to be "I know I remember my Catholic friends in school going to their confirmation classes, so..." :) But Alex already answered that one.
And if I may follow up, I was wondering if there was any counterpart to my sinner's prayer, the point at which one becomes a "believer". It sounds like for the Catholics, this might be the confirmation. After the classes and the rite are completed the person then knows enough of the basics and is able to give a reason for his faith, etc. Is that right? Is there anything like that for the Orthodox?
Perhaps another way to come at it is would you say there is any "need" for the sinner's prayer? I can't imagine you all would have any problem with saying a prayer and inviting Christ into your lives as Lord. But, is it needed, or is it not really needed because the same thing is already accomplished via sacrament? Is the idea of actively inviting Christ into our lives a part of your faiths? (Please don't take offense if this line is ridiculous. :)