What exactly is Electromagnetic Radiation? I don't understand how and why the electric and magnetic fields oscillate in the electromagnetic radiation wave, and any way where do these fields originate from, for there are no charged particles in the wave (there are no particles in it at all). Till now I've taken this for granted that the electric and magnetic fields oscillate at 90° to each other but recently I'm trying to study quantum physics but due to this confusion I couldn't understand it.
 A: Part of the genius of Maxwell was to realise that it did not require the presence of currents or charges to generate a magnetic field. In analogy to the way that changes in magnetic field generating an electric field (or macroscopically we say that changes in the magnetic flux linked with an electric circuit can produce an EMF and hence a current), it turns out that changing electric fields can also produce magnetic fields.
Hence electromagnetic waves can propagate in a vacuum without the need for charges or currents - the changing electric field begets a time-dependent magnetic field and this changing magnetic field begets a time-dependent electric field, and so on.
You also ask where these waves/fields come from. Well yes they do require currents or charges to produce them in the first place. More specifically they require accelerating charges. For instance a good approximation to plane polarised electromagnetic waves can be produced using an antenna in which an A.C. current flows - the charge in the antenna will be accelerating and decelerating rather than moving with a steady velocity. Strictly speaking this produces spherical wavefronts, but at a large distance from the antenna they would appear to be plane waves.
Finally you ask whether you should learn about Maxwell's equations. Of course the answer is yes, but usually Maxwell's equations (in their so-called differential form, which is what is required for a full understanding of the generation and propagation of EM waves) are not encountered until year 2 of a typical (UK) undegraduate physics degree.
A: For a classical discussion on waves I would refer you to review the Wikipedia site on Maxwell's equations first and then also to discussion on the Continuity equation for the purpose of understanding conservation laws.
Now for the quantum part.  
First we need to get you up to speed on what a field is.  Simply put it is an abstraction used in physics to assign a value to each point in space and time (or spacetime for relativists).
This assigned values generally have four categorizations.  The value can be:


*

*a scalar (e.g. just a number)

*a vector (e.g. an number with direction)

*a tensor (e.g. a object that assign values to all directions and their correlations)

*a spinor (e.g. a complex vector)


The electromagnetic field is actually the union of the electric field and the magnetic field.  It is the first example of a gauge field.  Gauge fields are the fundamental components of modern physics.  As I have [reviewed previously](adapted from David McMahon)5:

If temperature is viewed as a field, then at each point in the room,
  the temperature takes on a definite value. So as you walk through a
  room, you might feel a change in temperature, which can be understood
  as the field changing its value. An important additional
  concept is the idea that the values of the field are governed by some
  set of equations, and even though we can change the values of the
  field, the equations that govern them do not change.  This is captured
  with the concept of gauge
  invariance which is interpreted to mean that the equations of a
  field do not change under certain transformations called gauge
  transformations. Gauge transformations can be categorized
  as being one of two types, global and local. A global transformation
  does not depend on space or time. This is basically the same thing as
  saying that you can change the values of the the field $ \varphi $ in
  such a way that the change is exactly the same for every point in
  space and every moment of time instantaneously, or basically you add a
  constant everywhere for every time. Essentially, global
  transformations are generally undetectable since everything has
  changed everywhere for all time. This type of transformation leaves
  the underlying equations unchanged, but is generally
  uninteresting. Local gauge transformations are transformations
  of the field that do depend on space and time. These type of
  transformations also have the property of obeying special relativity,
  meaning that transformations are not going to effect distant objects
  faster than the speed of light. In order to create local
  transformations that leave underlying equations invariant, we
  introduce an auxiliary field $ A_{\mu} $, or hidden field, that is
  called a gauge potential, which is also called a gauge field. The
  gauge field lets us define an object called the gauge
  covariant derivative $ D_{\mu} = \partial_{\mu} - iA_{\mu}$ which
  can act on a field $D_{\mu}\varphi = \partial_{\mu}\varphi - iA_{\mu}\varphi $ and leave  the underlying equations governing the
  field unchanged (the $ i $ is used to tell us the gauge field is
  imaginary).

It can be argued that the combined electromagnetic field gains its waviness from the requirement that its Lagrangian (e.g. the equation that governs the fundamental relationship between the systems kinetic and potential energy) be Lorentz invariant (e.g. respect special relativity) under continuous transformations (e.g. a change in observational viewpoint of arbitrary precision).
Maxwell's discovery was that the electric and magnetic fields exchanged energy as a wave propagated in space.  Solutions to the Lagrangian under the constraints of gauge invariance are in fact a type of simple harmonic oscillator.
With that understanding, we have to understand that in the context of quantum mechanics, every field actually does have a particle associated with it.  In the case of the electromagnetic field, the particle is the photon.
In quantum mechanics, the "waviness" of the field is not actually manifested directly as an observable object.  Instead the waves associated with the particle exist in an abstract Hilbert space which is an infinite vector of complex numbers.  The wave encodes the probability amplitude (square root of probability) of detecting a photon at a given time in place.  The manifestation of the wave is only observable when considering large numbers of particles.  This is evident from the double slit experiment which shows the appearance of the wavy nature of underlying quantum field after the accumulation of multiple particle detections.     
A: There exists a very good formulation in this blog entry of Lubios Motl on how classical fields  emerge from quantum theory, .
The link between the quantized photons and the classical field are the Maxwell equations , Classical solutions of the equations give rise to the classical fields. Used with the operator formalism the wavefunction describes a photon. The square of the wavefunction gives the probability of finding the photon at (x,yz,t). It  carries not only the frequency nu of the classical field in its energy E=h*nu but also phases connected with the classical vector electromagnetic potential. 
In a handwaving sense, the classical field is not chopped up into photons, but it emerges as a synergy of photons with appropriate phases and energy connected with the frequency. The phases ensure that the long range interference patterns seen and explained with classical waves are also the probability wave patterns that even single photons display through the double slit experiment.
