Fixing a Position
It obviously takes more than one satellite to fix a position. One satellite will only locate a point somewhere on a circle (actually it is a sphere projecting outward from the satellite and appears to be a circle as it hits the Earth. To be more exact we can add another satellite. If we do so we now have two circles that intersect. But the nature of circles is such that they generally intersect in two places (two spheres will intersect each other in an entire circle intersecting the Earth in two places). This means that we need at least one more satellite in order to find out which point is the right point.
This information could then give us the latitude and longitude at which the device finds itself. To get really precise, and to give elevation or altitude we can add one more satellite. Taking a reading from four satellites will allow the four virtual spheres produced by the radio waves to come to a point in one place. This will fix the position exactly at least relative to the known positions of the satellites. Thus, with enough satellites in the sky we can fix our position almost instantaneously from any place on Earth or even above the Earth.
This whole process is actually quite similar to the way mariners once found their way around on the great wide oceans. Only these mariners used stars to calculate their circles. They used highly accurate chronometers that were kept in sync with the time at an observatory in Greenwich, England. At a certain time, just after twilight, sea captains would take fixes on stars based on where they should have been relative to the time in Greenwich. They would draw circles (actually lines - the charts were not big enough to encompass the circles) based on where the star actually appeared relative to the horizon. Where three lines crossed was where the ship was located on the terrestrial sphere. For best accuracy they would draw four lines based on four different stars.
As useful as this process was, it had tremendous disadvantages in comparison to the GPS system. First, it could only be done once per day in the early evening. Second, it required many complicated computations that were subject to error. Finally, a cloudy evening could completely eliminate the possibility of even a daily fix. Finding a location based on GPS is much faster because the computer does all the calculations. It is more reliable because it takes away the chance of human error and it can be used any time of the day or night and even in cloudy weather because it relies on radio waves rather than line of site.
Now that this technology has been developed and there are satellites surrounding the earth, there are many products available to make our lives easier and safer.