One of the principles Baptist churches have always valued was the "autonomy of the local church".
From a strickly "historical" view, Baptists in America have said this about "baptism":
American Baptist Historic Confessions
To sum it up, they essentially said:
"Baptism is an ordinance of the Lord Jesus, obligatory upon every believer, wherein he is immersed in water in the name of the Father, and of the Son, and of the Holy Spirit, as a sign of his fellowship with the death and resurrection of Christ, of remission of sins, and of his giving himself up to God, to live and walk in newness of life. It is prerequisite to church fellowship, and to participation in the Lord's Supper."
Abstract of Principles, James P. Boyce, 1858, Section XV: Baptism
It is summed up best here:
"
Person, Place, Timing and Setting for Baptisms
The Baptist concept of the priesthood of all believers indicates that any believer priest authorized by the local congregation can perform baptisms, not just a pastor or someone who is ordained. In most Baptist churches, the actual practice is for the pastor or a church staff member to perform baptisms. Some Baptists have insisted that only those who have been “called to preach” should baptize.
When possible, a public place is preferred by Baptists for baptism since baptism is a type of public profession of faith. A variety of settings have been used. In the past, most persons were baptized in rivers or lakes. For example, Sam Houston was baptized in a creek near the Independence Baptist Church. In more recent times, churches have built baptisteries inside buildings. Many other places continue to be used, however, such as swimming pools, lakes, rivers, ponds, creeks, oceans and even animal watering troughs.
Baptists opt for no particular timing in regard to baptism except that baptism is to follow a person’s conversion. Since baptism is not essential for salvation, there is no requirement to baptize immediately upon a person’s profession of faith. Some churches baptize very soon after a public profession. Others have a practice of asking the candidate to participate in a class for new Christians before being baptized.
Baptists regard baptism as a church function. In fact, Baptists believe that every person who is baptized ought to become a member of a local congregation. Baptists consider baptism not so much as an individual act but as one involving a community of believer priests, that is, a church. In a sense, baptism symbolizes a covenant between the person being baptized and a church.
Conclusion
Baptists, believing strongly in religious freedom, respect the right of others to baptize in whatever way they choose. Similarly, Baptists want to exercise our right to express our convictions.
Baptists in the past endured terrible persecution for their commitment to believer’s baptism. Surely Baptists of today will hold fast to believer’s baptism, never taking it lightly, making every effort to assure that the generations to follow understand its vast significance."
Link
Like I said, Baptists have always defined what baptism is, why baptism should take place and, who are the proper subjects baptism.
That is my position, and I stand by it.
God Bless
Till all are one.