From Reformed Layman:
The Covenant of Grace
Presbyterian: “Very well then, I give you the following biblical principles. If each of these be accepted, then my burden is met and the matter resolved.
1st God entered into a covenant with Abraham. This covenant was the Covenant of Grace. In it, God established a visible, discernable, body of people that would be his peculiar possession (Genesis 17).
2nd This body of people, the nation of Israel, was in fact the Church in Old Testament times.
3rd In those times, the sign and seal of the Covenant of Grace was circumcision. This ceremonial rite was administered as a rite of initiation into the membership of the Church (Genesis 17:10, 11). This outward circumcision of the flesh was symbolic of spiritual circumcision of the heart, or regeneration.
4th The Church was explicitly commanded to administer this rite of initiation to their infants.
5th In New Testament times, God having removed the shedding of blood from our worship, has replaced circumcision as the sign and seal of the Covenant of Grace with baptism. This outward washing speaks of inward cleansing and renewing of the Spirit, in short, regeneration. Both Baptists and Presbyterians agree that this is now the ceremonial rite of initiation into Church membership.
6th Throughout Old Testament times, the Church was required to administer the sign and seal of the Covenant of Grace to their infants, and thus receive them into Church membership. And so, unless it can be shown from scripture that our Lord or his Apostles purged the Church of infants, or barred Church membership to Gentile babies that had long been granted to Jewish babies, we must assume that the obligation to receive them through the rite of initiation still exists. For, just as we cannot add to the command of the Lord, neither can we diminish from it.
Read more: http://reformedlayman.com/Baptism/BaptismConversation.htm