Look up in the sky on a clear night soon and after a while you'll see a "star" moving across the background of the constellations. You're looking at one of several thousand satellites orbiting Earth. Satellites are a new phenomenon for sky watchers. Among the first really visible ones for people to watch were the Echo series - basically giant Mylar balloons intended to have radio signals bounced off of. These passive radio communication devices launched in 1960 have since been superseded by far more sophisticated transmitters, but their size made for impressive reflections.
Sheer size isn't the only way a satellite appears bright. A newer class of medium size satellite called Iridium uses solar panels that are reflective to the point that their light flashes are notably brighter than any other satellites, or even planets. Figure 1 shows how bright an Iridium flare can be. This picture was taken by Randy Brewer.
Figure 1 - A very bright Iridium Flare
You can tell a lot about a satellite simply by looking at it's path and speed across the sky. Some will move in a North to South (or vice versa) direction. This type of orbit enables a satellite to view virtually every location on Earth. This works well for any kind of Earth observing satellite. Look at the weather satellite photos on the next evening news and you're likely to be viewing the fruition of something operating in this polar orbit.
Large objects such as the International Space Station or the Space Shuttle use the more standard East/West horizontal orbit to take advantage of the Earth's rotation. The momentum given by Earth enables a rocket to place a satellite into a horizontal orbit with much less fuel than would otherwise be the case. Lofting a large payload into a polar orbit, in comparison, would take much more fuel, hence more weight, needing more rocket power, which ultimately means a far, FAR higher cost. That's space economics. Figure 2 shows a picture of the shuttle taken from the ground with an 12" telescope.
Figure 2 - The Shuttle Atlantis as seen from earth
How high is an object in the sky? It's a matter of relative motion to us. For a satellite to move into a higher (farther) orbit, it needs more speed. But that is not what our eyes see. For us, the closer an object is, the faster it appears to be - everything else being equal. The Shuttle, being only about 100 miles or so up, will move across the sky far more quickly than the weather satellite moving in it's polar orbit 600 miles in altitude. Higher means "slower".
Most satellite spottings tend to be strictly by chance. Yet we don't have to rely on dumb luck to see one. The orbital mechanics of the satellites are precise enough to make their viewing highly predictable. One source of predictions is the Heavens Above web page. Enter your location and you're a few mouseclicks away from finding the next International Space Station pass or satellite appearance in our part of the night sky.