You did not said anything about the software you are using. I will offer an explanation for ArcMap from the ESRI GIS suite.
Depending on the scale of the map, the boundary lines will be placed almost exact, or approximated. For an almost exact placing you will need a map with at least a scale of 1:5000. Use a current topographical layer from arcgis online and try to find common places that appear on the 1960 map and current topography; road intersections, buildings, waterways, railroads, etc.
Here is a how to interpret the transformations available for georeferencing. The higher the order of the transformation, the higher the number of points needed.
For more details, be more specific on your question after you use google and don't find anything relevant there.