Considering that I had my first Command in 1972 and at that point stopped taking sights and compass errors and further that I have been retired now for nearly 8 years, I may well have got this wrong.

Needed the name of your celestial body and a time GMT plus position Lat. and Long.

From the nautical almanac you can take the Greenwhich Hour Angle (GHA). If your celestial body is a star you will also need to note down the Sideriial Hour Angle, (SHA). yes and almost forgot the bodies declanation.

With the GHA and SHA and your Long it is a simple matter to work out your Local Hour Angle (LHA)
GHA + SHA +/- Long = LHA If the LHA comes out at over 360 degrees, simply subtract 360.

Having your LHA , declination and Lattitude go to your Nautical tables and look in the ABC tables.
Using the LHA, Dec and Lat in Tables A and B you will have two numbers this you take into the C table and it gives you a third number. This is basically your azimuth Lets say it is 059. If your dec is North the the azimuth is N 059 degrees, east if the body is rising and west if setting.. So that would make it either 059 or 301 degrees. This is the true bearing of the object. Set it against the compass bearing which you took at the begining and you will have your compass error. Apply the variation to this and you have your deviation.

Hope that I have got this right as it is all from memory.