I understand the connecting white and black wires. What do I do with a green grounding wire and copper grounding wire that is attached to the light fixture?
So you are removing a light and putting an outlet in?
Simply connect the ground to the ground screw on the plug. It is no different than how you connect the black or white wires.
If you are confused because there are two grounding wires but only one screw, then either use a grounding wire nut or twist the grounds together in such a way that you have one sticking out further then the other. Then you just put the tag end on the grounding screw.