1) Getting Started - GSOC
There's nothing difficult about observing satellites; you just have to know where and when to look. One way to get accurate predictions is to use the German Space Operations Center's website at http://www.heavens-above.com. This site is in Germany, and access has been reliable and fairly speedy.
GSOC has a database of cities, or you can manually specify your location. If you don't live near any of the database cities, you'll have to figure out your latitude and longitude. A good map will work, or you can try the web. MapsOnUs (http://www.MapsOnUs.com) works for US locations. Just enter a street address and the map engine shows its best guess as to where you are. You can set it to show the latitude and longitude of any point on the map.
Once you know your latitude and longitude, you'll need to enter this info at the GSOC site. Follow the instructions, and don't forget to select your time zone from the provided list. If you then bookmark the page after you enter your info, (the site indicates when to do this), the info will be recorded for the next time you enter the site.
2) What You'll Find
The GSOC site gives predictions for a number of satellites, including Shuttle flights, the ISS and Iridium. The ISS is the International Space Station now under construction. Iridium is a group of 70 or so communications satellites which are interesting to observe because they have mirror-like surfaces and can reflect a very bright beam of sunlight, a phenomenon called a flare. You can get predictions for the next 7 days for Iridium, and for the next 10 days for the ISS. Because orbits slowly change with time, it is best to get new predictions on the day you plan to observe.
3) How To Use The Predictions
The GSOC prediction chart tells you where to look in elevation and azimuth.
The Iridium satellites are all in polar orbits, and so pass over us going either N to S or S to N. The Shuttle, the ISS, and other non-polar satellites can go in almost any direction across the sky.
Predicted maximum brightness is specified in magnitudes. Lower numbers are brighter, and 5 magnitudes equals a factor of 100 in brightness. (A mag 0 is 100 times brighter than a mag 5, a mag -5 is 100 times brighter than a mag 0.) The fainter stars of the Little Dipper are about mag 5, Venus at its brightest is about mag -4. The brightest Iridium flares, at mag -7, are very impressive.
The brightest part of an Iridium flare only lasts a few seconds, but you can see the satellite for several tens of seconds before and after the flare. The ISS and most other active satellites usually do not show flares, just a bright moving spot. Discarded rocket boosters and dead satellites can tumble, and so will appear to brighten and dim in a regular pattern as they move across the sky.
The prediction times are accurate to a few seconds. You can get your exact time from the satellite predictions page or from the US Naval Observatory clock site at http://tycho.usno.navy.mil/time.html.
For more information on observing satellites, go to the Visual Satellites Observer's Home Page at http://www.satobs.org/satintro.html.