I am trying to replace my refrigerator plug. When I stripped the wires back, I found two wires made of several strands of copper. There is no color coding. In the center is a strand covered in green. I know that green is for ground, but how do I know which to attach to silver and which to brass on the new plug?

You would probably be better off buying a pre made pigtail and installing the whole new line. It may cost a few more dollars, but without electrical experience, it would be worth the cost. You should be able to look on the fridge and see where the pigtail lands on it. I have seen pre made pigtails that have ring terminals already attached to the fridge end. They should be fool proof.
If you must use the wire that is there, then I would trace it back to where it lands on the fridge and use a multimeter to check continuity between the 2 ends of the wires. The neutral and ground may also be landed together at the fridge.
But I would recommend the pigtail. Hope this is helpful.

Look at the wire. With zip cords, one wire is smooth, one is ridged. The ridged side is neutral and goes to the silver, smooth to brass.