How does a magnet cause magnetic force and its magnitude/direction?

Magnetic fields are created due to electron spin in the magnet. But how exactly does an electron "spinning" create forces around the magnet? Also, the magnetic force on a charge moving in the magnetic field is $qvB\sin\theta$, and its direction is perpendicular to the field and velocity of the charge. Why are these two facts true? I read the explanation for how magnetic force arises next to an electric current ( How do moving charges produce magnetic fields? ), but does the special relativity argument apply to magnets?