teering by the stars, finding routes and locations by them, and orienting oneself from the positions of celestial bodies is the ancient art of Wayfinding,or non-instrument navigation.  People have been wayfinding since the beginning of history because the stars are (relatively) fixed markers. This page will concentrate on the theory behind modern celestial navigation, what is called "modern," "mathematical," or "instrument" celestial navigation. 

Just about everything on theory and practice is in Bowditch's American Practical Navigator Online, but it's not an easy place to start. I will try to make this page as concise as possible.

The basic theory behind Celestial Navigation is simply that we find our unknown position from a known position. If we have some information, we can deduce the rest.

For example, if we know we are three miles from a flagpole, we could be anywhere on a circle with a three-mile radius and the flagpole as its center. If we knew the bearing of the flagpole (the compass direction, such as 135 degrees or Southeast), we could fix our exact position on the circle.  Or if we knew bearings from two objects spaced a reasonable distance apart, we could draw straight lines on  a map or chart  along those bearings from each, and where the lines crossed, there we are.

   This is fairly easy to do on land or on the coast, where we can find our position from known landmarks on charts and maps. On the open ocean, it's a different story, as there are no landmarks.  We can't take a bearing from an object as distant as the sun or a planet, because the compass is too clumsy an instrument. It measures in degrees, while a sextant measures in degrees, minutes, and seconds (there are 3600 seconds in a degree).  [The sextant does not give us a bearing, or azimuth, to a celestial body, but gives us information that helps us find the azimuth].  

The stars pretty much stay in the same place - that's why they were known as the "fixed stars" throughout history, except they rise and set; the sun, moon, and planets move, but predictably, and so with the aid of almanacs that tell us precisely where each body is at every second of every minute of every hour of every day of the year, and the practice of "sight reduction" (see Practice), we can take a position from two or preferably three stars, or planets, or the sun and moon when both are visible, or the sun at different times of the day, and where the lines of position cross is where we are.

Before going on to Practice, this is what you need to know:

*GP - imagine a string stretched from the center of the earth, through its surface, and into the center of the celestial body. The point at which in passes through the earth's surface is its geographical position. This information is in the Almanac.

*AP - The spot chosen as a reference point upon which to base our calculation. It is reasonably close to where we actually are if we base it on "dead reckoning" (having kept track of our position by recording speed and direction). Explained further under Practice.

*Declination - see Navigational Astronomy. Similar to the earthly coordinate latitude, it is the star's distance in degrees above the celestial equator.

Finding latitude by Polaris, and taking noon sun sights, do not require solving the navigational triangle. They involve simpler right triangles. For example, the sun at noon - real noon, that is, when the sun is at its highest point, on our meridian - is either due north or south of us, and our line of position is then due east or west. An east-west line is a parallel of latitude. These two are easiest to teach beginners. A simple explanation of latitude by Polaris is available (however, it does not include reference to the corrections that are necessary because Polaris is not precisely North, but a bit under a degree away). See also here - historically interesting.