How do I determine which ceiling fixure wires are which (two black, two bare)?

I'm trying to install a basic light fixture on a switch, but the ceiling wires are not color coded, probably because it's an old house.

The ceiling box has two black wires and two bare wires. One of the black wires actually appears to be two wires spliced together.

Any ideas on which wire is which or how I can determine this?

Update:

I got a hold of a non-contact voltage tester and found the live wire. The wall switch has no impact on which wire is live.

There was a working ceiling fan installed here before. I'm not sure how it was hooked up though. Is there a way to determine which wires are which now that I know which one is live?