I believe that astro can be best understood by dealing with the method, sight taking, and sight reduction (the calculations) separately.
Decide Method
There are many ways in which the observed data can be used:
 Noon Sight for Latitude
 ExMeridian sight for Latitude
 Equal altitudes for Longitude
 Longitude by Chronometer (a form of Time Sight)
 Time sights with position determined by Sumner Lines.
 Double Chronometer for Latitude and Longitude  time sights.
 Marc St Hilaire Intercept method  known as the New Navigation.
 Double Altitudes. Various methods, includung mixing Sumner lines and the intercept method (aka New Navigation.)
 Intersecting circles of equal altitude.
 Lunar for time and longitude
Take Sight
 Measure altitude of celestial object above the horizon.
 Measure altitude of celestial object using an artificial horizon.
 Measure altitude of celestial object using a bubble sextant.
 Measure altitude of celestial object using an esoteric device such as a Bris sextant.
Reduce the Sight
There is a plethora of ways in which a sight can be reduced:
 Longhand with mathematical tables.
 Short methods using tables.
 Inspection tables.
 Slide rules, including the Bygrave and the German MH1.
 Electronic  calculator, phone app, spreadsheet or online calculator.
