Here are the major perspectives on baptism, what it is and does, within Christianity, really briefly:
- Baptist (aka Zwinglian)
- Baptism is purely symbolic. It does not do anything except make a public statement about what your new identity in Christ. It comes after salvation and plays no role in the process. It should be by full immersion, and only administered to professing believers.
- Reformed (Modern)
- Baptism is a sign and seal of the covenant of grace. It does not save you, or contribute to your salvation, but the Holy Spirit uses it to reassure you of the grace you have already received. It makes you a member of the visible Church, and should be administered to the children of believers just like circumcision was for Israel. Immersion is not necessary; sprinkling or pouring is acceptable.
- Reformed (Classical/Calvinian)
- Baptism is mysteriously related to regeneration (new birth). While baptism does not automatically regenerate, and people can be regenerated without baptism, regeneration and forgiveness usually happen alongside baptism for those who receive it in faith. Apart from faith, baptism does nothing. It should be administered to infants, for the same covenantal reasoning as the modern Reformed view.
- Baptism saves, not by itself but because it is accompanied by the Gospel. Baptism is a real symbol; it is the Gospel in the form of a physical act. Those who receive it in faith are born again and forgiven all of their sins. The Word of God and the Holy Spirit do the real work: baptism is just one form of the Word. Because the power is in the Word, immersion in not necessary, and sprinkling is fine. It should be administered to infants for the sake of their salvation.
- Churches of Christ
- Baptism saves, not by itself but because it is your response of saving faith. Faith without works is dead, and the first work of faith is baptism. You are saved by grace through faith at baptism. Immersion is mandatory. It should not be administered to infants because they cannot respond to God in faith.
- Roman Catholic
- Baptism saves by the principle of ex opere operato (“from the work worked”). The act of baptism, simply because Jesus has commanded it, cleanses from past sins and original sin and brings someone into the Church. Salvation is, however, not completed at baptism. Penance and confession are necessary for sins after baptism. Immersion is not necessary; sprinkling is perfectly fine, if not preferred. It should be administered to infants to remove original sin.
Well, those are the major positions. Some less common perspectives on baptism, such as Federal Vision and Eastern Orthodox positions, are both too rare and too similar to others listed for me to bother mentioning. For Bible verses on the topic, see here.