We describe simple experiments that allow students to observe, identify, understand and measure different noise sources always present in photodetection systems: amplifier noise, thermal resistance noise (Johnson noise), and photon noise (shot-noise). With a suitable low noise amplifier and a commercial photodiode, students can verify the dependence of photon noise versus light level. This photon shot-noise is directly related to the quantum << nature >> of light and it has long been considered as a fundamental limitation of the optical photodetection systems. It is sometimes mistakenly described as due to the detector itself. We show that it is possible, with fairly affordable laboratory teaching equipment, to measure a photocurrent with a noise power below the shot-noise level using a suitable light source. More precisely, using a photodiode and a high-quantum-efficiency light-emitting diode driven by a constant current source, we can observe a reduction of the photon noise power of about 0.8 dB below the shot-noise level.