An observer determines their latitude by measuring the altitude of an astronomical object at the time of its meridian transit.
This is usually done with the equinox Sun at solar noon to determine the observer's latitude, but can be done with any celestial object.
In short, the zenith distance of a celestial object at meridian altitude is the difference in latitude between it and the observer.
The estimated time of meridian altitude of the heavenly object is extracted from the nautical almanac.
A further correction must then be taken into account to counter the "wobble" of the earth's spin and rotation relative to the sun and planets.