Thankfully, some of them hire professional cartographers like me, either directly or through book publishers.

I typically begin by making a basemap of the unchanging underlying landforms, using datasets like Natural Earth Data or The National Map in ArcMap/ArcGIS. Onto that, I'll overlay information from historical maps or from written descriptions. Sometimes I'll georeference a detailed 19th century map in ArcMap, but more often I immediately move the project over to Adobe Illustrator and align various overlays "by eye" there, drawing additional features by employing my experience and knowledge of what's most reliable from the different sources. Is the modern course of that river most probably where it was in 1880, or should I trace the line that was shown in an atlas of that era? How could that factory have been miles from the nearest railroad line in 1910? Which corner of the intersection was the union hall on? Did the streetcar tracks run down the middle of the road or beside it? Beyond geographic research, what addresses were being used in the 1870s and how do I convert those to modern house numbers? Should places be named and spelled as they were at the time—Constantinople, Siam, Pittsburg—or with modern placenames? What transliteration should be used for placenames not in Roman script: Peking or Beijing; Rangoon or Yangon? Does this university press use Hawai’i or Hawaii? And beyond all of that are the usual cartographic questions of how many grayscale tones will be distinguishable when printed on soft paper, what size type will be legible, what symbols and lines can be easily understood by readers.

Of course, GIS software is now pretty accessible to most graduate students, and increasingly they will try to prepare their own maps using ArcGIS or open-source equivalent QGIS. They may even realize that to prepare the maps for reproduction they'll need to do finishing work in Illustrator or open-source equivalent InkScape. But they commonly overestimate how much historical geodata is available—we don't even have all that many historical country boundaries —and they may not think of all the issues involved in doing quality historical cartography.