In order to acomplish such a manicure one needs a dotting tool. The famous dotting tools... I have always dreamed of having such nail tools, they look so... professional :-)
On a second thought, a dotting tool is just a stick with a round edge! So I came up with my own, home made dotting tool, which looks like this:
My home made dotting tool is made of a traditional pencil with a gum on it, in which I have stuck a decorative needle.
With this needle, the size of my polka dots will be like the ones on this picture:
If you want bigger dots you can use a bigger needle. If you want smaller ones you can use a bobby pin or the tip of a used ball pen. I recommend using only fully used ball pens, you don't want to ruin you manicure with some left over ink.