How to connect earth(grounding) that has copper wire attached?
The bare copper wire is a "pigtail" that exists to make your connection to the light fixture easier. I'm guessing that you have a metal junction box (which requires its own ground connection). 

Simply nut your fixture's ground wire to it. The key is that all grounds are connected to the panel. It's usually not critical what the actual path is as long as the connections are sound.