Magic.
Or
If you want the 'classical' faraday/maxwell answer they're produced by alternating the direction of an electric field (inc. in a material)
Thats not really an explanation though. It doesnt give a mechanism.
If you want the quantum mechanical (well, the quantum electrodynamics to give the field, no pun, its proper name) explanation then its that certain atoms have a net spin (spin being a quantum property/quantum number that all charged particles have), because theres a leftover from all the spins of the particles its composed of. All charged particles have a positive and a negative varitation of the spin the particle is capable of carrying and all available energy levels are occupied once for each available spin (see fermi principle for an explantion). If you have a leftover spin then you can find the magnetic field moment
m = g.Q.s/2.m
Where q ia the charge, m is the mass and g isnt normal g, its 'g factor' which I've forgotten everything about except that its dimensionless and s is the spin (1/2 or 1, positive or negative, zero is a possible spin but gives no magnetic moment).
If this happens then photons (virtual photons, that you cant see, they just exist nebulously as a feild) move through the atom in the direction of the net spin and in proportion to the m, magnetic moment.
Which means that magnets are all made of molecules which are themselves magnets. A magnet is also therefore definitionally anisotropic. Any magnetic molecules are non-isotropic (they have an asymmetry because of their spin whereby they make a magnetic field in a particular direction) and a 'magnet', i.e. any lump of stuff that has a magnetic field has a magnetic field because some proportion of the magnetic atoms or molecules in it (assuming that it contains non magnetic atoms and molecules, which it will) are facing the same way.
If all of them are facing in random directions then all directions are equally magnetic and their is no net field. This would be isotropic.
Sorry for the maths. Really, I am.
And for any of the more scientifically literate members (I know youre there!) for any errors - its been a while since I did QM. Please correct if you spot anything.