The key components are the two transistors connected back to back. The first (Q1, pins 1, 2 and 6) is effectively used as a zener diode which will exhibit breakdown noise at low currents [1]. The second transistor (also labelled Q1 but on pins 3, 5 and 4) is used as an amplifier of said noise.

A similar circuit is explained in more technical detail here: http://www.nutsvolts.com/magazine/article/bipolar_transistor... (look for the "WHITE NOISE GENERATORS" chapter title)

[1]: https://en.wikipedia.org/wiki/Noise_generator#Zener_diode