Maxwell's equations are the right answer here. There is a more accurate quantum mechanical theory of electrodynamics, but the quantum corrections are not really relevant.
If you want steps, it goes like this:
At first (assuming we start from zero electromagnetic fields), there is a current [tex]\vec{J}[/tex], but there is no magnetic field [tex]\vec{B}[/tex]. By
[tex]\frac{\partial \vec{E}}{\partial t} = c^2 \nabla \times \vec{B} - \frac{1}{\epsilon_0} \vec{J}[/tex]
a nonzero electric field is created. Then that electric field will produce a nonzero magnetic field, which in turn produces an electric field even further away from the source, and so on, creating a propagating electromagnetic wave.
You can describe this stuff in terms of photons as well, but that would be more complicated and not really more fundamental; after all, quantum electrodynamics fundamentally describes the world in terms of
fields, getting particles as a result, not a postulate.
Theheretic said:
If the oscillating electrical/magnetic fields form the radio wave then where does the photon/particle concept come from? If an EM wave is nothing but electric field and magnetic field oscillating at right angles then how can a "particle" magically form out of this?
Unless you view the photon as a wave packet of the burst of oscillations, is that what a "photon" really is then? Just a packet of close frequency oscillations of electric/magnetic fields?
In the full quantum theory, one can calculate that an electromagnetic wave, much like an atom, can only have a certain discrete spectrum of energies. But unlike an atom, the energy difference between each possible level is the same: [tex]\hbar \nu[/tex]. If the electromagnetic field is in a state other than its ground state, we say there is one or more photons present.
A comment: Feynman's QED lectures/book is very, very good for giving a conceptual understanding of
quantum mechanics. But despite the title, it doesn't do a very good job with QED. He completely skips the treatment of the electromagnetic field and electrons as fields, and launches directly into Feynman diagrams, which are best understood as an calculable approximation scheme to the field theory. So if want to learn QED, you'll need a quantum field theory textbook, and yes, it is hard.