Including the reference on the map layout is considerate to your fellow mapmakers, who may look at your map and wonder, "Wow, that's some great data! Where can I get that for my own maps?"
My goal is to make it as unobtrusive as possible, so as not to distract from the main point of the map.
One way is to combine acknowledgments with other uninteresting but necessary information ( eg coordinate reference system) in a single line in a small font at the bottom of the map, eg:
Or you can include reference/copyright info next to the layer name in the legend:
Regarding "how specific?" I like to be as specific as will fit on a single line. If I have many sources of data, I would condense it as much as possible. For example, Google Maps displays copyright info at the bottom of the map. Multiple sources of imagery are lumped together, while 'map data' is listed separately.
If the map is full-page, there should be room on the page for a single line. For smaller inline maps, include acknowledgements as you would references, eg as footnotes, or footnotes pointing to a reference section at the end of the article.