Reddit reviews 2017 Nautical Almanac

The sun's position in the sky is constantly changing, including its declination (latitude). Every year navigators buy themselves a new Nautical Almanac which allows them to work out the sun's declination at any time during the year to the nearest 600th part of a degree (tenth of an arc-minute). In turn this allows them to determine latitude to the nearest tenth of a nautical mile, though difficulties in observation and other sources of error mean that being within half a nautical mile is good work.

Once you have the sun's noon (maximum) altitude in degrees above the horizon (corrected for several sources of error) and you've worked out the sun's declination at the instant of that observation (using the Almanac), working out your latitude is not much more than subtraction. You have to be careful about whether the sun's declination is north or south and whether you are north or south of the equator, but it's no harder than keeping track of plus and minus signs during any arithmetic. No trigonometry is required here.

Longitude from noon sights comes from working out what time of day the sun was highest. You have to stand there with the sextant for several minutes watching the sun go up and then down. You might take several timed readings and later work out when you think it reached its highest altitude. This time, plus the sun's longitude (SHA from the Almanac) give you your longitude. At the equator four seconds corresponds to a nautical mile so it's challenging to be more precise than that.

See this sample spread giving the position of the sun, moon and planets every hour for a three-day period. There are further tables at the back of the Almanac that make it easy to interpolate the figures to come up with an accurate position for any time during the hour.