How would I measure that I'm at a pole?
You could confirm with taking an image of the star trails.  They would form a circle with the apparent center at the zenith of the location.  You do not need a pole star at all.  Just a night of viewing.

You would also be able to tell based on the height above the horizon that the sun is.  On the equinox, the sun would be on the horizon at noon (when it is at its maximum height).  On the summer solstice, its angle will be above the horizon equal to the angle of precession.  And below by the same amount on the winter solstice.  

Measuring latitude using the sun

For any other day in the year, you will need to determine the max angle based where you are between the equinox and solstice.

Compensating for the Earth's tilt

Basically, you would determine if you were at a pole the same way you determine any other latitude.  You are just looking for a result of 90 degrees.