The critical first step is polar alignment, which means making sure the 'right ascension' axis of the mount points exactly at a point above the north pole. This is done (on my setup) by looking through a special finderscope aligned with the axis and placing polaris at the right point (calculated by time and date) on a circular scale (to allow for it being slightly away from the pole).
Once this is done the mount will move (if I have it balanced right) with far more accuracy (the resolution is about 0.75 arc seconds) than I can point it for setting up! Most targets are big (the Rosette nebula is nearly three times the diameter of the moon), the apparent size of the Horsehead is about ten times the size of Jupiter at its biggest.
But yes, if the setup is poorly balanced I can end up with photos of the wrong part of the sky. A few quick test pictures usually confirm all is OK, for faint targets you just check the star pattern.
I suggest downloading the free programme 'Stellarium' which will give you an excellent way to choose targets for observation.
Neil