If you're new to a polarizer, the effect can be so subtle as you rotate it that while it's working you don't see any difference.
Convince yourself something is happening by looking through the lens with the polarizer on and pointing it at an LCD monitor (which emits polarized light). The result will be very dramatic and you can make the screen go completely dark.
Here's where I'd turn to some book learning. Light: Science and Magic - An Introduction to Photoraphic Lighting has an excellent write up, with pictures, that shows the behaviors of light and polarizing filters. It will illustrate that the polarizer will cut glare, but not reflections.
With this knowledge, walk out to your car and point your lens at your car's windshield while the sun is out. Turning the polarizer will make the bright glare go away, allowing you to see more clearly into the car.
The same effect can be seen with sunshine bouncing off of water, say on a lake or river. In some cases, you can visually penetrate the surface and see into the water's depths, depending on angle.
In each of these cases, the effect is going to appear more and more subtle, but because you're learning what to look for, the slight changes are going to be far more obvious.
If you point your lens at the sky and rotate the polarizer, you should see the sky getting progressively darker then progressively lighter again. What's often missed is that this effect is dependent on where the sun's direction is relative to where you're looking. So if the sun is behind you, you may see nothing at all. If the sun is 90 degress to you, it may appear drastic. (And obviously, avoid looking into the sun with remaining eye.)