How did the Puritan community define and regulate sin?
The Puritans who left England, first to seek religious freedom in Holland (most lived in Leyden) and then to America, defined sin in general as rebellion against God and, by extension, God's authorities on earth. If virtue is obedience to God laws, as set forth in the Old and New Testaments of the Bible, then man's assertion of his self will, of independence from God, is ultimate sin. For example, man's most important sin--the sin that damned mankind until Christ redeemed mankind with his death--occurred when Adam took a bite of the apple in Eden, a complete abrogation of his duty to obey God and an exercise of willful disobedience through self assertion.
As soon as the Puritans arrived in what is now Massachusetts in 1620, acting in accord with the Mayflower Compact, which most had signed before disembarking, they established a civil and religious society based on man's dependence upon and subservience to God's laws--in essence, Puritans agreed to deny any form of self assertion (freedom to act according to the individual's will) in order to create a society controlled by God's laws.
Because of the Puritan's belief in the Covenant of Grace--God's agreement to accept Christ's redemption of man's original sin--Puritan leaders understood that the Church, rather than civil authority, must guide its members behavior and punish mis-behavior--to "regulate" sin, in your words. Puritans who wanted to formally join the church were required to insure the church membership that they had experienced God's grace and were therefore prepared to accept God's laws as a guide for their behavior in both religious and civil matters. In this way, the church became the de facto rule of law in the community and extended its control from religious to civil life. Even though English Common Law governed the colonies, including the Massachusetts Bay Colony, a violation of civil law was, more often than not, considered a breach of religious law.
Puritan settlements in Massachusetts had both civil and religious leaders, but the religious establishment had a significantly greater influence over the daily lives of both church members and those who chose not to formally join the church. The regulation of daily life, then, was, for the most part, in the hands of Puritan church leaders, and the punishment of sin, which included severe corporal punishment, was in their hands.