Identifying old armored electric wire and mounting new fixture
The big thing is figuring out which wire is switched hot and which wire is neutral. Note that it is possible, due to messed up wiring, to have some other combination, such as hot and a switched neutral, which would not be a good thing.
Use a non-contact tester to:

Verify that both wires are &quot;dead&quot; with the circuit breaker (or fuse) off. If not, stop and ask a question. (There can be false positives, but really shouldn't be on a simple fixture connection, as opposed to wires in a box with a bunch of other wires).
Turn on the breaker. Verify that both wires are &quot;dead&quot; with the light switch off. If not, stop and ask a question, as you may have a switched neutral.
Turn on the switch. Identify which wire is hot. This wire is the switched hot. The other wire is the neutral. Mark the neutral wire with white tape.

Turn off the breaker. Wire nut the light fixture hot (typically black, but could be any color except white, green or bare) to the switched hot wire. Wire nut the light fixture neutral (should be white) to the neutral wire. Turn on the breaker, test.