It can be random, but often it results when one circuit picks up another's signal. To keep noise to a minimum, you need to reduce the efficiency of both generators and receivers of noise. Most of the sources of random noise are either resistors or semiconductors and tubes. The thermal energy of electrons produces noise in every resistance, even if it is not connected to anything. Any current flow in a tube includes noise, because each electron strikes the plate at a slightly different moment.
Semiconductor junctions have a similar problem.
These sources are fundamental to circuitry, and it's difficult to reduce the noise they produce. You can, however, reduce all types of pick-up. These can affect circuits in many ways. They often seem random, but there is always an underlying cause. If two traces are too close, current can flow directly between them.