I've heard people talk about the Decretive, the Preceptive, and the Permissive wills of God, but I don't entirely understand them. What do they mean and what makes them distinct from each other?
The decretive will of God is where God decrees what definitely will happen. For example, if God decrees that Jesus Christ will return in judgment, then that will definitely happen.
The preceptive will of God is where God gives us a precept. This is how we see what God desires us to do. For example, all of the Ten Commandments show us the preceptive will of God. The difference is that while God tells us to obey the Ten Commandments, He doesn't decree that we will definitely obey them, thus "permitting" our disobedience.
Charles Hodge, in his Systematic Theology, says the following:
The decretive will of God concerns his purposes, and relates to the futurition of events. The preceptive will relates to the rule of duty for his rational creatures. He decrees whatever he purposes to effect or to permit. He prescribes, according to his own will, what his creatures should do, or abstain from doing. The decretive and preceptive will of God can never be in conflict. God never decrees to do, or to cause others to do, what He forbids. He may, as we see He does, decree to permit what He forbids. He permits men to sin, although sin is forbidden. This is more scholastically expressed by the theologians by saying, A positive decretive will cannot consist with a negative preceptive will; i.e., God cannot decree to make men sin. But a negative decretive will may consist with an affirmative preceptive will; e.g., God may command men to repent and believe, and yet, for wise reasons, abstain from giving them repentance.
Preceptive will, permissive will, and passive will are synonymous. Decretive will, sovereign will, and active will are synonymous.
The Westminster Shorter Catechism questions and answers 7 and 39 say the following:
Q. 7. What are the decrees of God?
A. The decrees of God are, his eternal purpose, according to the counsel of his will, whereby, for his own glory, he hath foreordained whatsoever comes to pass
Q. 39. What is the duty which God requireth of man?
A. The duty which God requireth of man, is obedience to his revealed will.
Q&A 7 describes the decretive will of God. Q&A 39 describes the preceptive will of God (more or less).
It is worth noting that in Reformed theology, there is only one will of God. However, the word "will" has two meanings, and thus there is the will of God in the definition of will whereby God ordains something and causes it to come to pass, and the will of God in the definition of will whereby God requires and commands something of mankind.