Both believers and their children are included in God's covenant love. Children of believers are to be baptized without undue delay, but without undue haste. Baptism, whether administered to those who profess their faith or to those presented for Baptism as children, is one and the same Sacrament. The Baptism of children witnesses to the truth that God's love claims people before they are able to respond in faith. (Book of Order W-2.3008)
Baptism, therefore, usually occurs during infancy, though a person may be baptized at any age. Parents bring their baby to church, where they publicly declare their desire that he or she be baptized. When an infant or child is baptized the church commits itself to nurture the child in faith. When adults are baptized they make a public profession of faith.
The following list is taken from the Book of Order W-2.3004
the faithfulness of God
the washing away of sin
rebirth
putting on the fresh garment of Christ
being sealed by God's Spirit
adoption into the covenant family of the Church
resurrection and illumination in Christ
Unlike some denominations, Presbyterians do not require a person to be entirely immersed in water during baptism. Baptism is received only once. Its effect is not tied to the moment when it is administered, for it signifies the beginning of life in Christ, not its completion. The Presbyterian Church (U.S.A.) believes that persons of other denominations are part of one body of Christian believers; therefore, it recognizes and accepts baptisms by other Christian churches.
Baptism is almost always administered as part of a worship service. In the Presbyterian Church (U.S.A.), baptism must be authorized by the session of a particular congregation and performed by a minister.