How do the sacraments become effectual means of salvation?

The sacraments become effectual means of salvation, not by any power in themselves, or any virtue derived from the piety or intention of him by whom they are administered, but only by the working of the Holy Ghost, and the blessing of Christ, by whom they are instituted.[1]

1. I Peter 3:21

   Baptism, which corresponds to this, now saves you, not as a removal of dirt from the body but as an appeal to God for a good conscience, through the resurrection of Jesus Christ.

   Acts 8:13, 23

   Even Simon himself believed, and after being baptized he continued with Philip. And seeing signs and great miracles performed, he was amazed. For I see that you are in the gall of bitterness and in the bond of iniquity.

   I Cor. 3:6-7

   I planted, Apollos watered, but God gave the growth. So neither he who plants nor he who waters is anything, but only God who gives the growth.

   I Cor. 12:13

   For in one Spirit we were all baptized into one body—Jews or Greeks, slaves or free—and all were made to drink of one Spirit.

Question 161, Westminster Larger Catechism