electromagnetism - How do magnets work?

I've read a classbook on the field theory (including EM): it perfectly describes quantitive patterns in EM-theory, but I have no luck understanding how and why it works.

I mean, magnetic substances are described mainly by magnetic moments of electrons, but all explanations of the phenomenon I've found are rather of deep high-level focus on fields exclusively, than on explanation why it works and what underlying mechanisms bring all those ideas to life (including explanation of what field is, except that it is an abstraction).

So, the question is: may anyone try to give (or point to) a popular and thorough explanation of magnets and on low-level mechanisms, which unifies and explains how this long-distance interaction really works (i.e., not only modelled and described mathematically)?

p.s.: also, I'd like to see some papers on computing magnetic properties of bodies (iron ball, for example, finite plane, NeoCube's ball chains, etc).

Thanks in advance!