Need to replace a receptacle... was two prong. It blew up. The wiring behind it has only two brass wires wrapped in black insulation. There are no other wires and no way to tell the two apart.

How would I wire a 3 prong receptacle to this? I plan on marking and covering the ground and using it with non grounded cords.

You need a tester, two actually.
One regular tester to check for the proper voltage and the other a non-contact tester. This you just place near the wire to check for the presence of voltage. This will tell you which is the hot and which is the neutral.

A better solution to your problem would be to either use a new two-prong receptacle (YES, they are available), or better yet would be to install a GFI. The GFI WILL function properly even with no grounding mean present and will be safer than a non-grounding receptacle.