Many people have never imagined that it is possible to spot an orbiting satellite in the sky.  Many of you could have already seen an orbiting satellite but just didn't realize it.  Here is what you could do to find and observe an earth orbiting satellite: 

First, find out if a satellite will make a pass in a location which you will view it.  To find out when this occurs, just find out the satellite predictions for your area.  To find out satellite predictions, use these links:

In these web resources, all you have to do is enter your latitude and longitude and it'll automatically generate a satellite prediction for your area.   To find your latitude and longitude consult a map of your area with specific latitudal and longitudal lines.

http://www.chara.gsu.edu/sat.html   This page produces a list of the visible satellites in your area after you enter the longitude and latitude.

http://www.gsoc.dlr.de/satvis/  This page makes predictions for many satellites around the world, including the Mir spacestation and Iridium satellites that are known for their bright flashes when light reflects off of them.

http://liftoff.msfc.nasa.gov/realtime/JTrack/   This page lets you track satellites on your computer.

http://liftoff.msfc.nasa.gov/RealTime/JPass/   This page also gives satellite predictions and gives a great graphic of the prediction.

http://acsprod1.acs.ncsu.edu/scripts/HamRadio/sattrack   This page tracks specific known satellites and predicts passes in your area.

http://www.bester.com/satpasses.html   This page makes predictions of satellite passes in North American cities.

Second, find out the altitude and brightness if possible.   Remember the higher the altitude of a satellite, the less visible it is.  The brightness is measured in the same way that the brightness of stars are measured.   Certain parts of the satellite reflect light better, for example the solar arrays act almost like a mirror.  Also, the size of the satellite affects visibilty.   Obviously, the smaller a satellite is, the more difficult it is to see.  Most importantly, if the satellite is passing through the earth's shadow, it is nearly impossible to see it because the light from the sun is being blocked.

After you have obtained an accurate satellite prediction, you should, naturally, go out and try to observe it.  While is is possible to see a satellite with the naked eyes, it is always better to use a visual aid.  A binocular will dramatically increase the visibilty of the satellite.  A 50mm (diameter of lens) binocular is most suitable.  An 80mm reflector telescope will further increase visibilty.  However, make sure you have a motor driven mount on the telescope to accurately track the satellite.

Lastly, while trying to observe the satellite, make sure you have a starfield guide because that will allow you to locate the position of the satellite amongst the stars.  This way, it would be much easier to spot the satellite if you knew where to look in the sky.

Enter this page for more information:

http://www.satellite.eu.org/sat/vsohp/satintro.html