Genesis 9:3

"Everything that lives and moves will be food for you.  Just as I gave you the green plants, I now give you everything."  Genesis 9:3

Here God is giving mankind the right to eat meat.  Presumably, before this point, men were all vegetarian.  There is also no commands about what meat we can eat or not eat, although even before the flood there was an understanding that some animals were clean and others were unclean.  In Genesis 8:20 it tells us that Noah sacrificed clean animals to God and even before that in Genesis 7:2 and Genesis 7:8 scripture tells us that there were both clean and unclean animals going into the ark before the flood.

According the BibleAsk God allowed man to eat meat for several reasons.  This article suggests that it was because of the food shortage from plants a global flood would have caused and possibly to limit the life span of mankind.  Whatever the case, it was from this point on that we are allowed to eat meat - something that I am extremely grateful for.