The same mechanism with as a spray bottle. Compressed air blows out from outside the paint nozzle and the air at the tip of nozzle gets pushed away. This creates a vacuum condition and paint gets suctioned out.
This process atomizes the paint into a mist of tiny particles.
This is the most popular method today.

Airless spray gun applies a high pressure to paint which discharges through a small nozzle. When doing so, air is forced into the paint to atomize it. Overspray is minimal and large spray patterns are possible. This method is efficient and able to handle high viscosity paints.

Electrostatic painting is a method based on the principle that the positive and negative electrical charges attract while like electrical charges repel each other. The paint is charged negatively in a high voltage generator while the body is charged positively as it is grounded. Since paint particles from the paint applicator are charged negatively, they repel each other and are atomized. These negatively-charged particles are attracted by the positively-charged body and adhere to it.