DOT: A tiny round mark made by or as if by a pointed instrument; a spot. - thefreedictionary.com
This is such a simple method that I always think everyone already knows how to do it, but I think that's just me, who comes from a crafty background. Growing up we were constantly exposed to art, painting and crafts of many variety so things like this come by second nature without a thought. But then the thought did come to me that some of you may not realize how fast and easy a project can be when you're adding painted dots - which you might be dreading. Dread no more!
Dotting in the artistic world widely referred to as Pointillism, a form of making art out of a series of dots. There are many different styles and representations to using this in art. Notice in the "Morning Shave Dot Painting" (above) uses a grid-like technique similar to that of a closely viewed newsprint image, and heavy to light areas with spaces of negative space or white space to create the overall look. As you can see between the two images [above] Pointillism or Dot Painting, can easily fluctuate between more abstract and loose like the flowers in the first painting.
Pointillism is a technique of painting in which small, distinct dots of pure color are applied in patterns to form an image. Georges Seurat developed the technique in 1886, branching from Impressionism. The term Pointillism was first coined by art critics in the late 1880s to ridicule the works of these artists, and is now used without its earlier mocking connotation. - -en.wikipedia.org
image credit & copyright artist, giddygirli from flickr.com
It can also be as basic as this image. There is no limit.
Regardless of using this dotting method for an artistic piece or a craft piece they can easily be reproduced using the eraser end of a pencil, the rounded nubby end of a paint brush (or other nubby-type stick-like object), an artist or nail art dotting tool, or a stiff round [paint] brush. I personally opt for the first two options as with any more or less pressure on the rounded brush my increase or decrease the diameter of your dots and if you want an equal even set that doesn't work. Also, using a brush and getting the angle off can vary the size and shape of your dots. Realistically, you don't need to go out and buy a dotting tool, they are handy, yes, but there's probably something in your house that you already own to be able to make dots with. It's easy.
The last TIP I'll leave with you is to first practice practice practice on a scrap piece of paper before delving right in to it. Generally, to get the same size dots for each one, you would want to dip and re-dip for each one, make sure you don't get too much paint globbed on to your dotting tool (whichever you decide to use). Sometimes even dipping-dotting your tool in to the paint, and then do a single dot on a scrap paper can release the initial glob of paint it grabbed and make nice rounds.
Paintbrushes, with their rounded, aka "nubby" ends, tend to make smaller and smaller dots as you re-use the same dip. An eraser on the other hand would more likely just get more faded and start creating rings or uncertain outcomes with each re-use of the same dip.
The paintbrushes will also leave a more bubbled look like this image (above) when using the end of a paintbrush (or a round paintbrush used for making dots) or an actual dotting tool. Even more so, using a latex gloss paint over a flat paint, may affect the end finish "bubbled" look as opposed to a flat dot-circle look. Leaves you with lots of experimenting to do! Good luck!