In many of my answers I continue to stress the same point: READ LANDAU!
The reference you want is volume 4, section 2, "quantization of the free electromagnetic field". You must however fully understand volume 2, section 51, "The Fourier resolution of the electrostatic field".
Let's briefly review the main idea of quantizing the electromagnetic field.
First of all, in the theory of the quantum harmonic oscillator, the energy levels are quantized; and a very convenient mathematical method is to use the raising (creation) and lowering (annihilation) operators (which raise and lower the energy level by 1).
The Fourier coefficients of the electromagnetic field correspond to the creation and annihilation operators for creating and destroying photons of a given energy.
This physical interpretation of the quantization process distributes the energy of the electromagnetic field in discrete energy packets (photons), just like in a simple quantum oscillator.
When quantizing the electromagnetic field, it's best to work with the Heisenberg picture of quantum mechanics, which is based on Poisson brackets, and not the Schrodinger picture. The idea is to put the field equations in terms of Poisson brackets, and then to apply the rule that a Poisson bracket becomes a commutator for operators.