The first law of reflection says simply that the angle of the incident ray and the reflected ray are always the same, `theta_I = theta_R` .
To show this experimentally, we need three things: a laser, to give us well-defined incident rays of light, a mirror, to reflect off of, and some form of sensors or detectors that allow us to measure the angles.
Then, we point the laser at the mirror at various known angles, `theta_I` , and measure the angle of the light that comes off the mirror, `theta_R` . We can't actually see the rays, but we can measure where the light hits our detectors and extrapolate what the rays must have been, thereby determining the angle. (We could also put this whole apparatus in a cloud chamber and almost actually see the rays — what's really happening is we've essentially set up millions of detectors right in a row.)
If the first law of reflection is right (and it is), the reflected ray and the incident ray should have the exact same angle, within the margin of error of our experimental setup. In fact, this law is so thoroughly empirically supported that if we don't get that result, we can basically be sure there is something wrong with our experimental setup, and have no reason to actually doubt the first law of reflection.