Who instituted the practice of sacrifice? Sacrifice plays a very important role in the Bible.  One of the earliest stories, that of Cain and Abel, begins with two sacrifices.  The death of Jesus on the Cross was a sacrifice.

Here is how the first sacrifice is described, in Genesis 4:3-6:


  In the course of time Cain brought an offering to the LORD from the fruit of the ground, while Abel, for his part, brought the fatty portion* of the firstlings of his flock. The LORD looked with favor on Abel and his offering, but on Cain and his offering he did not look with favor. So Cain was very angry and dejected. Then the LORD said to Cain: Why are you angry? Why are you dejected?  


Does the Bible ever say who first instituted this practice, and when? The purpose animal sacrifice is discussed [here] 
 (What was the purpose to animal sacrifices?).
Did it develop naturally?
Was it instituted directly by God, through a command?
Do we know?
According to several sermons I've heard, the first animal sacrifice was recorded in Genesis 3:21 (KJV).


  Unto Adam also and to his wife did the Lord God make coats of skins,
  and clothed them.


He used the skin of some animal to cover their nakedness.



One source for such a teaching is at Sermoncentral.com.


  The First Sacrifice is recorded in Genesis 3:21.
  
  Remember the setting? Adam and Eve sinned against God, their eyes were
  opened, they realized they were naked, and they were ashamed. So they
  tried to cover their nakedness with fig leaves. But fig leaves make
  lousy clothes. So God intervened, sacrificed an animal, and make
  garments of skin for them.
  
  This is the first sacrifice mentioned in the Bible. An innocent
  animal, most likely lamb, lost it’s life so that Adam and Eve could be
  covered.


Thus, as with all of God's institutions, it was established by God Himself.