Of course, any accelerated charges radiate electromagnetic waves.
On a fundamental level there is only the electromagnetic field written as two three-dimensional vector fields, \vec{E} and \vec{B} or, more elegantly, as a antisymmetric Minkowski-space tensor field, the Faraday or field-strength tensor F_{\mu \nu}. On a microscopic level, a solid is described quantum mechanically (or in classical approximation) as a lattice of atoms bound together through electromagnetic interactions.
Under usual circomstances you can treat the problem in the Born-Oppenheimer approximation, i.e., (for a body at rest) as a lattice of atomic nuclei, to which the electrons are bound. In metals you also have conducting electrons that are (quasi-)freely moving.
Now, if you perturb this static system in thermal equilibrium by shining in an electromagnetic wave, this wave acts via the Lorentz force,
\vec{F}=q \left (\vec{E} + \frac{\vec{v}}{c} \times \vec{B} \right )
on all the charges. Approximately the bound electrons start to vibrate around their equilibrium locations, and the conducting electrons start to drift and thus make an induced AC current. This in turn radiates em. waves which superpose with the external em. wave you shine in.
Of course, you cannot resolve the details of this highly complicated macroscopic problem of the self-consistent motion of particles and fields in all detail. Fortunately this is often not necessary, but you can coarse-grain over distances large compared to the spacing of the atoms or molecules in the lattice, provided the typical wavelength of the incoming radiation is large compared to the lattice spacing. Further, if the magnitude of the external em. field is small compared to the em. field of the charges making up the body, you can calculate the reaction of the matter in linear approximation ("linear response theory"). What you get from this is nothing else than "macroscopic" electrodynamics with the coarse grained electromagnetic field (\vec{E},\vec{B}) and the auxiliary fields (\vec{D},\vec{H}) that are connected with each other through the dielectric tensor and magnetic permeability tensor which for isotropic media even simplifies to scalars. The auxiliary fields turn out to include the reaction of the medium in terms of polarization and magnetization, and the charge and current distributions in the macroscopic equations are only those external sources added to the medium in equilibrium.
You find an excellent treatment of macroscopic electromagnetism from this modern perspective, providing a much better physical understanding of the meaning of the various quantities than in the usually given purely phenomenological treatment, in the Feynman Lectures, vol. 2.
Of course, if the external electromagnetic wave is chosen in the infrared frequency range, despite the reaction of the bound and conducting electrons you also excite lattice vibrations. Here also the same concepts hold, and the macroscopic em. field can be understood as the superposition of the imposed external fields and the fields created by the motion of the lattice ions.
