How things radiate electromagnetic radiation? I don't ask why they radiate (higher temperature than 0K) but how they radiate this electromagnetic waves?
Answer
There are two ways of getting electromagnetic radiation from matter.
Matter is usually neutral, the electrons and protons are equal in number to each other and any fields are spill over giving rise to Van der Waals forces which bind neutral atoms into molecules etc.
At this micro level nature is quantum mechanical. That means that all electrons are in energy levels some of which energy levels are practically a continuum, i.e. the difference between them is very small. This means that vibrations of the atoms and molecules in their solid structure, as an example, will excite by kinematics these levels and fall back by the emission of a photon ( de-excitation); the ensemble of these photons gives rise to black body radiation. When the temperature is high the corresponding energy levels have larger gaps, and the photons are of higher energy.
A filament lamp has high enough temperature to emit visible light . Liquids have similar behavior, gases only have molecular energy levels and vibrations but the process is the same. Kinetic energy from temperature is transformed into photons from de-excitations .
The bulk of light we see comes from this mechanisms, even the light from the sun.
There are the LED lights, again a quantum mechanical effect, but of different origin:
"when electrons cross the junction from the n- to the p-type material, the electron-hole recombination process produces some photons in the IR or visible in a process called electroluminescence."
The second way of getting light is how the other answers state, by accelerating charges, ions and electrons, as in sparks and lightning, plasma etc.
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