This is a question that was drastically changed and the other answer and the comments to the question and the answer are discordant with the edited question.
I already advised in the comment that you read a simplified article in wikipedia on electromagnetic radiation. Classical electromagnetic radiation cannot be simplified easily by analogies. I will try to explain with the quantum mechanical framework which is the underlying framework for all physics, classical theories emerge from this framework smoothly.
The electromagnetic wave is composed by a huge number of photons. Photons are elementary particles, they have zero mass, are point particles and their energy is characterized by the frequency of the classical wave we observe macroscopically, given by
In addition photons obey the Maxwell Electromagnetic equations in their quantum mechanical form. This means except their spin and energy they are characterized also by the vector potential entering the Maxwell equations.
You must have no problem accepting how a single photon can travel in space, even in vacuum. It is a quantum mechanical particle which will go in a straight line if it finds nothing to interact with. Single photons have been measured by making laser beams very faint so that only one hit happens on the detector at a time. They even have commercial single photon detectors.
The question goes into how zillions of photons can build up the electromagnetic waves that come to us from the stars, for example. They add up in a similar way that water molecules add up and make up streams, except in smaller dimensions and faster times. A stream of photons arrives continuously from those stars with the impetus given when they left so long ago.
If the light is coherent, i.e. the disparate constants describing each photon mathematically have a fixed phase , the individual fields, E and B described macroscopically with a wave equation, can be seen schematically:
This 3D diagram shows a plane linearly polarized wave propagating from left to right. Note that the electric and magnetic fields in such a wave are in-phase with each other, reaching minima and maxima together
The wave is built up by zillions of photons in step so that their spins, and other constants describing them build up the macroscopic wave, even though it is made up of all these elementary particles, all going in a straight line unless they hit something on the way.