How can I turn off the power so I can safely replace a fixture?
Tom, if the spotlight still lights up, it might be sufficient to just turn off the light switch leading to the fixture. That's assuming the power enters the switch box, and there's only a hot and neutral (and ground) going to the light fixture. Tape the light switch in the off position and tell everybody to leave it alone until you're done.  ;-)

Or you can just flip breakers until the light turns off.

But even then, you have to consider the possibility that there is still power at the light fixture. Who knows what might have been wired through that same box by who-knows-who in the past?

You really need to get yourself an electrical tester. If you get the standard old solenoid-type tester (the old "wiggy" style--"Wiggy" is actually a trademark from 1918) then you have to expose the wires so you can touch the test leads directly to them.

You can pull the light fixture away from the wall or ceiling without disconnecting the wires, to give you access to the wires for testing.

If you don't want to have to disconnect wirenuts and expose the metal wires, you can get a non-contact electrical tester which can detect current from the electromagnetic field from outside the wire insulation (these units work because a weak but harmless electrical circuit is still completed between you and the ground--electromagnetism is pretty amazing).

Get something like one of the images below, which you can find for anywhere from $5 to a few hundred. Play with the tester a little bit with a couple of live circuits, or with the cord on a plugged-in lamp or something until you feel confident about how it works, then try your circuit breakers one by one until you can't detect any live wires in the light fixture box.

Then (trust me), tape the breaker in the off position with a note on it so nobody turns it back on to make toast while you're handling the wires.