Due to predictable conditions of satellite movement in space (lack of atmosphere) computer software can calculate a satellite's position for given moment. Calculations are done based on known orbit parameters determined at epoch. Known orbital parameters like inclination, eccentricity, argument of perigee, mean motion (revolutions per day), let us track satellite for a reasonable period of time after epoch. Orbital data for each object is grouped, and distributed as a Two Line Element (TLE) file.
To keep tracking software working precisely, one should update elements periodically. For low orbiting objects (altitude less than 500 km) TLE data should be updated every few days. For higher orbits, you can update your TLE every few weeks. Other important things include making your predictions as close to real time as possible by using time synchronization, and the precise coordinates of your location.
You must remember that TLE data for an object that has maneuvered since the last elset is no longer any good. Updating is most important for satellites like Progress, Soyuz, and the Space Shuttle which maneuvers often (docking, deorbit, changing of orbit).
Why do we track satellites? There are several reasons. One might want to observe (even with the naked eye) ISS passing over their home or brilliant Iridium flares. Radio amateurs use satellite tracking software to obtain the best pass for QSO with another radio amateur. Such software can help you with your hobby, and will help you understand more about Astronomy, and Physics. So even if you're a beginner, don't hesitate to download satellite tracking software like Orbitron. Change your home into mission control center!
Remember, satellite tracking is the easiest ever with Orbitron!