I don't know the polarity of my magnet. I don't know if it's north, south, or a different one on each side. How do I find out?

There are many ways to find out, and the easiest is to use a magnet which you already know the polarity.

Otherwise, you can make use of solenoid and power to generate an electromagnet and use that to check the polarity.

You could let the magnet hand freely (on water, or suspended by a light string) and let it rotate to align with the Earth's magnetism...

You can use a compass too.

And by the way, your magnet absolutely has both poles, north AND south. If you could come up with a magnet with only one pole, you'd be very rich and very famous!