First, paint the background color of your choice--a kind of a robin's egg blue was originally used. Then, using a stiff brush--cleaning brush, even a tooth brush, spatter the white. There are typically more white spatters than black. After the white dries, spatter the black. This is a very messy process. Be sure to experiment first and be sure to mask off anything you don't want to get spattered!

The original spatter paint is called Zolatone paint (thanks Ron S.) It is widely used in the boat industry today. See their website for more information.

And, thank you Alex, a rechargeable aerosol can, which can be purchased and used to spray on the Zolatone paint.