If I go to google sky - http://www.google.com/sky/
Ihere is a longitude and latitude measure at the bottom of the page. Iow are these coordinates determined and who sets it?
Do those coordinates move at all over time?
These coordinates are really called right ascension and declination
and they're the most widespread pair of coordinates to describe the celestial sphere. They're analogous to longitude and latitude on Earth but they're not quite the same thing.
See also other coordinates sometimes used in astronomy