Step 1: Nature and origin.
An electromagnetic wave is a self-sustaining disturbance of mutually perpendicular electric and magnetic fields, set up whenever a charge accelerates. A changing \(\vec{E}\) creates a \(\vec{B}\) and a changing \(\vec{B}\) creates an \(\vec{E}\), so the wave regenerates itself as it moves.
Step 2: Geometry.
It is a transverse wave; \(\vec{E}\perp\vec{B}\perp\) direction of travel, and the three form a right-handed set along \(\hat{E}\times\hat{B}\). \(\vec{E}\) and \(\vec{B}\) reach their peaks together (in phase).
Step 3: Speed and field ratio.
In free space every EM wave moves at \(c=1/\sqrt{\mu_0\varepsilon_0}=3\times10^8\) m/s, and at every instant \(E=cB\), i.e. \(E_0/B_0=c\). In a medium the speed becomes \(v=1/\sqrt{\mu\varepsilon}\).
Step 4: What they carry and how they behave.
They transport energy (Poynting vector \(\vec{S}=\vec{E}\times\vec{B}/\mu_0\)) and momentum, so they exert radiation pressure; the energy is split equally between the two field halves. They need no medium, are undeviated by external fields (being uncharged), and undergo reflection, refraction, interference, diffraction and polarization.
\[\boxed{\text{Transverse, no medium needed, speed }c,\ E_0=cB_0,\ \text{carry energy and momentum}}\]