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Fine alignment is only worth the bother for a permanently placed mount. The entire process can take several hours; you won't want to repeat it each night. Nevertheless, if you have a motorized mount and are able to place your telescope in the exact same position on subsequent night, the following are instructions for obtaining fine polar alignment of an equatorial mounted telescope.
The first step of fine alignment is to lock the telescope at the middle point of its declination axis and point it as the North Celestial Pole. Unfortunately, Polaris is close to, but not exactly at the Celestial Pole. To find the exact location of the North Celestial Pole, use the Tirion Sky Atlas 2000.0 or any good sky atlas. It is not absolutely necessary to use such a map, but it will save you time carrying out the last step of final alignment.
The last step is to pick out two widely separated stars and see how they wander from the field of view. The initial placing of the star within the field is done by adjusting both the declination and right ascension axes. Afterwards, the star is followed only by modifying the right ascension. During fine alignment, use your most powerful eyepiece and keep it pointed upwards. First find a star near the southern horizon. Place the star just at the upper edge of the field of vision so that any drift will be easily detected. Follow the star by twisting the right ascension knob as the star moves.
If the star drifts upward out of view then move the polar axis a bit towards the left and when the star drifts downward into the field, move the axis towards the right. Keep on doing this until the star remains exactly as the upper edge of the field of view. Now, repeat the process on a star near the western horizon, this time trying to keep the star at the right edge of the viewfinder. A drift of the star rightwards out of the field is compensated by lowering the polar axis. A leftward drift into the field is nullified by raising the polar axis.
Go back and forth from the southern to western horizon (you don’t have to use the same star each time) until there is no drift in either direction. You may adjust the polar axis by playing with the tripod's legs or by re-clamping the polar axis. Your telescope is now perfectly aligned.