How is electromagnetic radiation produced?

The classical view is that EM radiation is produced by (an) accelerating charge(s). The charge doesn't have to be an electron. This is fine in 'classical' situations (e.g. the production of radio waves from a radio transmitter as the conduction electrons oscillate).

But this doesn't work when you consider atomic-scale systems (including very short EM wavelengths) and you have to interpret the process using quantum mechanics (or more precisely, quantum electrodynamics). This treats EM radiation as photons; a photon is produced whenever charges in a system change state.

The 2 views (classical and quantum) are of course linked. The classical case is the limiting quantum mechanical case for a system in which the energy levels can be considered so close that they form a continuum.

You are very much on the right lines, but you are being a bit parochial about it.

Take a wider view and think about "conservation of energy". You know, the bit about "Energy cannot be created or destroyed but....".

When anything changes from a higher energy state to a lower energy state, >>something<< has to happen to the excess energy.

In the case of your electrons, that extra energy is often converted to e-m radiation and released as a photon. The bigger the difference between the two energy levels, the higher the photon energy, and therefore frequency, will be.

Quoting: "Firstly when a photon is absorbed by an electron and the electron is excited into a higher energy state."

That could be the case, if we are talking about fluorescence, etc, but unnecessarily limits the general point. In a practical case, you want to deliberately produce photons by exciting electrons into higher energy levels directly, either electrically, thermally or chemically for example, so that they emit photons when they decay back into their lower states. Think LEDs, fireworks, red-hot pokers.

The point about accelerating charged particles is a good one, but what you are saying is that you are adding or removing kinetic energy to/from your particles, and that energy has got to come from/go to somewhere. Using an alternating electric field to accelerate electrons backwards and forwards along an antenna wire perhaps?

I hope that hasn't just added to the confusion :-)