If computers process information in the form of "0" and "1" which is due to function of transistors. What is the signals from electromagnetic radiation processed as, example radio waves. How does a device take the input of radio wave and turn it into information?

Analogue signals like that are converted to digital values by an analog to digital converter (ADC). This converts the varying input to a series of digital values representing the voltage at each instant. 

A simple diagram of an ADC would look like this:

 

The eight output lines each output a 1 or 0,      Together they can output binary numbers from 00000000 (0) to 11111111(255).

The input is compared to a reference voltage and converted to an output value depending where the input is compared to the reference.

There would also be a "clock" input.   This is a signal that tell the ADC how often it should sample the input and change the output values.