Em dashes used as parenthetical dividers, and en dashes when used as word joiners, are usually set continuous with the text. However, such a dash can optionally be surrounded with a hair space, U+200A, or thin space, U+2009 or HTML named entities   and   These spaces are much thinner than a normal space (except in a monospaced (non-proportional) font), with the hair space in particular being the thinnest of horizontal whitespace characters.
1. (letterpress typography) A piece of metal type used to create the narrowest space.
2. (typography, US) The narrowest space appearing between letters and punctuation.
Now I'd like to see how the metal type looks like, but ehm... it's difficult googling it.
Also a whole collection of space types and what they're called in other languages.
In German you use en-dashes with spaces, whereas in English it’s em-dashes without spaces. Some people dislike em-dashes in English though and use en-dashes with spaces as well.
In English, typically em-dashes are set without spaces or with thin spaces when used to separate appositives/parentheticals (though that style isn't universal even in professional print, there are places that aet them open, and en-dashes set open can also be used in this role); when representating an interruption, they generally have no space before but frequently have space following. And other uses have other patterns.
In British English en-dashes with spaces is more common than em-dashes without spaces, I think, but I don't have any data for that, just a general impression.
