The subject is covered in much detail in our book Emergency Navigation, which covers not just the North Star, but how to find directions from any stars in the sky. The North Star is just a bit easier.
First and foremost, it will be due north, at a height above the horizon equal to your latitude. Another general way to think of it is it will be a faint star to the north, about halfway between Cassiopeia and the Big Dipper, but often this entire space is obscured by haze, which leads to the value of having many ways to find out where the North Star is, even when we cannot see it.
Here is one method based on Cassiopeia. These are all from Chapter 5 of the that text.
Figure 5-6. Finding Polaris from Cassiopeia. Any view of Cassiopeia alone will tell where north is. Find the nearby region in the sky from which the constellation would look like an M. Imagine a line along the base of the M. Twice that distance from the base at the trailing star of the M is the location of Polaris, even if the star happens to be obscured by clouds. Th e squares in the corners are reminders that this distance should be projected at right angles to the base. Directly below that point on the horizon is due north.
The next picture covers all those cases where the pointer distance is about 5 times the pointer length.
Figure 5-9. Ways to find Polaris. Any one of these widely spaced constellations will locate north. The + or – signs indicate that the polar distances are either somewhat more than or less than exactly five times the pointer spacings. However, it is simpler and adequate to just remember the factor of five—you point with your fi nger, each hand has five fingers. Stars at the bows of the constellations are the leading stars; those at the sterns are the trailing stars.
I hope that helps. Please see the book for a lot more on steering by the stars in the North and South Hemispheres.
The North Star is fairly faint (magnitude 2) but any of these pointers is just as good as the north star for finding the place where the North Star is, even when covered by clouds, as illustrated in the picture below: