I'm also trying to mount a ceiling fan.
Upon removing the light fixture, I discovered that there were 3 BX cables connected on top. Only ont of those bx cables has 3 wires comming out. I can really tell the color of the insulation, because it's the old kind of cloth type, and 2 out of the 3 cables look just the same. But the 3rd wire has a red cloth insulation.
How do I know what's what?
The other 2 bx cables, have only 2 wires coming out. I need to have them all connected, because one of the cables goes to a light in another room, and I believe the other goes to the outlet on the same room.
How do I connect them together?

 

If you can put everything back together exactly the way it was before you removed the light, then this job will be trivial. All you have to do it connect the fan to the same two wires that the light was connected to and leave all other connections alone.

If you cannot, this is going to be a protracted mess. We can help you through it, but it will take 100 times more effort than it could have been. First you will need to go buy a multimeter and a tick tester.

Please tell us you have the first situation. If not, post back when you have the multimeter and tick tester in hand.