How to find the position of a star in the sky

The RA and DEC of a star are fixed (except for small real motions) and don't depend on your position on earth or the date/time.
The set of stars visible overhead do depend on the date/time and position.

A good place to start is probably "Practical astronomy with your calculator"

 

converting from stellar (RA,DEC) to Earth coordiantes is fairly easy:
http://en.wikipedia.org/wiki/Celestial_coordinate_system#Equatorial_to_horizontal_coordinates

You also need the local sideral time, easiest way is to ge tit from here http://tycho.usno.navy.mil/sidereal.html [Broken]

 

Imagine a line starting from the center of the Earth and passing out through your head. When you look straight up, you're looking along that line. Due to the definition of declination, the declination of the star there is simply your latitude. The star's right ascension depends on where the vernal equinox is--and sidereal time tells you that, with 0:00 corresponding to it being at the prime meridian. Right ascension is the difference between your longitude and the sidereal time, converted to degrees. If your longitude is 70 degrees West, for example, and the sidereal time is 5:00 (75 degrees), that would mean the vernal equinox is 5 degrees to the west of the star. Right ascension would be 5 degrees.

Depending on the level of accuracy you want, you may have to account for precession. Since the Earth's axis is wobbling due to the torque of the Sun and Moon, the right ascension and declination of any star changes with time. Most star catalogues give coordinates valid for J2000.0: noon on January 1, 2000, so to get extremely accurate coordinates, you'd have to precess your calculated RA and Dec. to that epoch.

 

Are you interested in finding the formula, or deriving it? It would be a good exercise.

 

I've actually written such a program before, so if you have any questions, feel free to ask!

 

Well, if you want to derive it, how far do you want to take it? precession of earth? eliptical earth orbit?