How do we know that light is made up of electric and magnetic fields? What are the experiments that prove that light consists of electric and magnetic field oscillating perpendicular to each other. What are the experimental evidence we have for this theory of light ?
 A: Take a look at the Hall effect at the Hall Effect Wiki. It does not necessarily pertain to electromagnetic radiation, but the same general principle applies for all electromagnetism. See below for a general description for this relationship.
We use Hall effect ammeters to non-invasively measure the current through a wire. James Clerk Maxwell studied electromagnetic fields in the 19th century and compiled some of the most useful mathematical descriptions for electromagnetism. See: Maxwell's Equations. While these do not provide a physical description of why the fields are perpendicular, we can see that to accurately describe the fields through mathematics we are left with a solution with perpendicular fields. 
To see this for yourself, grab a Hall effect current sensor to measure the current through a wire. The sensor detects the magnetic field which is presumed to be perpendicular to the motion of charge. Compare the result to the traditional form of current sensing, which is to put a ammeter in series with the same wire in a circuit. If the fields were not perpendicular, you might find very different values for the current. We do not know your circuitry experience, so if you decide to try this make sure you know that what you are doing is safe.
If you step out of circuit theory and understand fields from an electromagnetics perspective (like with Maxwell's equations as opposed to Ohms law and the like), these fields apply to both circuits and free space. Whether you want to consider propagation of fields in free space or induction of fields or currents though other media, the same general principles apply. I'd provide more literature, but I do not have enough stackexchange reputation to post more links at this time.
Extra tid bit: There are special cases where one component of an electromagnetic field can be zero. In these cases the concept of direction becomes difficult to describe, since a vector with zero magnitude has no direction associated with it. Devices, such as waveguides, are designed to control how electromagnetic energy propagates through it. Some waveguides will have regions where the electric field component goes to zero, for example. In this case the fields are not really perpendicular, and therefore we could suggest that electric and magnetic fields are not necessarily always perpendicular. But this is somewhat of a stretch since it requires specific physical constraints that do not naturally occur.
