During the Protestant Reformation, the Reformers rejected the Roman Catholic seven sacraments and only embraced two sacraments as being those instituted by Christ: Baptism and the Lord's Supper. For these two sacraments, we have explicit evidence from Scripture that Christ instituted them for the church. Since we only do in worship what God commands, therefore we are not to multiply sacraments just because we think those extra "sacraments" are helpful or that others may have benefited from them.
What is a sacrament? The Westminster Shorter Catechism puts it this way:
Q 92: What is a sacrament?
A: A sacrament is a holy ordinance instituted by Christ; wherein, by sensible signs, Christ, and the benefits of the new covenant, are represented, sealed, and applied to believers.
(Westminster Shorter Catechism Q92)
A sacrament is instituted by Christ. The word "sacrament" is the rendering of the Latin translation of the Greek word normally translated "mystery" in New Testament. Therefore, the sacraments are visible signs pointing to the truths of God. As signs, they point to a deeper spiritual reality which we ought to meditate on. The sacraments are also seals, which mean that as we partake of them in faith (not apart from faith), we partake of the spiritual truths they point toward. God uses the sacraments to grant us more grace in our walk with Him on this world, so that we may be further strengthened to live our lives for Him.
During the Reformation, the Roman Catholic church embraced the idea that the sacraments work its benefits merely because they are done (ex opere operato), so that faith is not necessary. The Reformed view of the sacraments however is that faith is necessary in order to benefit from the sacraments. God is giving us a sign and a seal of his grace towards us, but as the sacraments are always God's relating and covenanting with us, therefore we as the recipients have to be involved in receiving His benefits with our faith.
Baptism is the rite of initiation into the covenant community. It marks the fact that a person is now to be considered as a partaker in God's Covenant of Grace. In the Reformed view, baptism is not a ceremony whereby the believer publicly confesses his faith before God, which is the Credobaptist view. Rather, baptism is the application of God's mark to the person that he or she is now a member in the covenant community. That is why the Reformed tradition holds to both adult and infant baptism. This is not because of church tradition (although the church has a long tradition of infant baptism), neither is it because of sentimental love for one's children but rather because of God's covenant of grace which is always to believers and their children (Deut. 30:6, Jer. 32:39, Ezek. 37:25, Acts 2:39).
Since adult baptism is done after an unbeliever comes to faith, it is natural for people to think that baptism has to do with one's faith. Thus, it is not uncommon that even among those who hold to infant baptism, infant baptism is thought of separately from adult baptism, as if the two are separate rituals altogether. But that is a false way of thinking. Both infant baptisms and adult baptisms are done on the same basis: that God is applying the mark of the covenant to the person. Adult baptism is done as the person by faith joined the covenant community, and thus baptism is more like a welcome ceremony into the church rather than a public declaration of personal faith. Infant baptism marks the inclusion of the baby or child into the covenant based upon the promises of God "to you and your children," and similarly welcomes the child into the community of the saints.
But, it may be objected, what if the child manifests that he has no faith in God when he reaches adulthood? Well, what do we do with adult converts who apostatize after they had been baptized? We excommunicate them. Likewise, children who reject the faith in their mature years would be excommunicated and kicked out of the church. Baptism is never administered because we believe the person is saved, for nobody knows the status of anyone's soul. The church can only judge a profession of faith, but never a person's faith or lack thereof. Therefore, adult baptism is administered to a person who makes a credible profession of faith and thus can be judged to have joined the covenant community. Whether any particular person is saved or not saved only God knows, and each one's faith would be manifest only at the final judgment.
Baptism is a sign and seal of the covenant of grace. It signifies one's entrance into the covenant of grace, for it is a command of God for all in the covenant community, believers, to be baptized. Baptism is also a seal of covenant inclusion, for in Galatians 3:27, those baptized into Christ have "put on Christ," which means that baptized believers now partake of Christ and have communion with Him.
This New Covenant sacrament of baptism replaces circumcision in the Old Testament (Col. 2:11-12), and is meant to signify the inner reality of regeneration (1 Peter 3:21). Therefore, the external rite of baptism is meant to reflect the inner reality of regeneration. It is therefore not uncommon in Reformed churches for believers to be told to remember their baptisms, by which they are to recall the sacrament of baptism being administered to them, so that they may be comforted in their afflictions that God is their God and we are His people.
In the Reformed tradition, the mode of baptism is not important, for the metaphors of sprinkling (Ex. 24:8, Heb. 9:19, Ezek. 36:25), pouring (Is. 44:3, Ezek. 39:29, Joel 2:28-9) and immersion have all been used to depict regeneration, which baptism signify. Since baptism is God's mark on His people, it should not be administered more than once. It is an objective mark, and therefore it matters not whether the person has faith at the time when he received the mark of baptism, as long as he currently has faith. The only consideration for "another baptism" is if the first baptism is invalid, which would imply that the person is actually going to be baptized truly for the first time and not actually being rebaptized.