You use MS Paint or some equivalent program.
That's the very low-tech way. The higher tech way is a bit more complicated, involving downloading GIS files and editing spreadsheets. It's an easier method to use when there are a lot of districts, like towns or even precincts or if getting out maps quickly is important, as on election day. (Though that's getting less important as newspaper and other reporting websites are getting more complex).
I can explain this in a lot more detail if you are interested.