Starbursts around bright point lights are mainly caused by diffraction at the lens aperture. In practice, the biggest control you have is aperture: using a smaller aperture (higher f-number) usually makes the starburst effect stronger and more defined, while opening the aperture (lower f-number) reduces it.

The shape and number of rays are also influenced by the lens diaphragm design, especially the number and shape of the aperture blades. Lenses with more rounded aperture blades tend to produce less pronounced starbursts.

Shutter speed does not create the starburst pattern itself; it mainly changes exposure. A longer shutter can make the light appear brighter overall, but the star shape is primarily from aperture diffraction and lens design.

A separate way to create a similar look is with a star filter, which adds the effect optically in front of the lens.