An example of a TLE for the international space station is shown below:
The numbers "03338" on the first line indicate that the epoch was on the 338'th day in 2003 (December 4th).
TLE's of man-made orbiting bodies are maintained by the North American Aerospace Defense Command (NORAD). This agency owns powerful radar and tracking installations which are able to accurately track these bodies.
In theory a TLE is able to predict the exact motion of a satellite for any point in the future. In practise, several factors cause the accuracy to degrade over time. These are (a) small errors in the initial measurement, (b) corrective manouvers performed by the satellite itself, (c) drag caused by the small amount of atmosphere still present at orbital altitudes, (d) effect of solar wind, (e) relativistic effects. Because of this, TLE's are updated by NORAD on a regular basis (the TLE for the international space station is updated several times a day.) Recently aquired TLE's are only needed for tracking a satellite to extreme accuracy - the TLE used for this project was grabbed on November 15th, and is expected to yield results accurate to within one degree of latitude and longitude for the next six months.