Actually, it is so awesome, there are a number of projects like that already on the internet. Like RCArduino (reading RC controller with an Arduino), or PPM RC to USB (reading RC controller's PPM signal).
But here, something different is required, something that reads the RC receivers signal to the servo, converts it to an 8bit value, and sends it over the USB port. That way, any receiver could be connected and any channel read.
So, step one, check how the signal of a RC receiver looks like:
It looks like a standard servo PWM signal (1ms for far left, 1.5ms for center and 2ms for far right), with no delay between switching from one channel to the next.