Here I am... no, over here. You see, ironically, as your GPS unit I have all the power in the world to find you, but you have almost none to find me. And that's because, contrary to popular belief, we GPS receivers do not send out signals of any kind. That's why we're called receivers, as opposed to transceivers or transmitters. So you'd better not misplace me.
How then, do I know where you are on the face of this planet and how fast we're traveling? Mathematics is the answer, and while the algorithms are fairly complex, the idea isn't. Imagine two friends stood 100 meters apart. If they both shout at exactly the same time it stands to reason that whoever you hear first must be closest. Hear both simultaneously and you must be in the middle.
Us GPS units work in a similar way. Each GPS signal transmitted from space contains unique information about where and when that satellite is.
I then listen for any signals and accurately record when they arrive. Because the speed at which the signal travels is known, I can then make assumptions about how far we are from the satellite that sent it. If I only received the signal from one satellite, I can only know that we're 'X' distance from that satellite – but I wouldn't know in what direction. We might actually be closer to the moon for all I know. Two satellites aren't much better either. Imagine two soap bubbles pressing together. There'll be a ring around them where the two bubbles join – and again all I can tell is that we must be somewhere on that intersecting point because that's the only place you could stand for the signals to arrive at the time they did (the satellites are at the center of each bubble).
To say with any certainty where we are in space. I need a minimum of four satellites signals. And I'm looking for the coordinates of a single point where all four bubbles overlap. Except we don't so much get a point, as much as a small area. And that's where accuracy comes in. Most GPS units don't know exactly where they are, just that they're somewhere within a 1 to 15 meters radius of a certain area.
Interestingly, I'm assured by clever people who build us, that to work out your speed we GPS units do not simply compare your position at time 'X' and your position at time 'Y'. Instead we use the Doppler shift in signals to calculate it. In the same way that police sirens change pitch when moving toward or away from you so the GPS signal shifts. And because of the accurate way in which the signal is times, it doesn't matter if your absolute location is accurate or not – your speed and distance traveled will be, because it's relative to itself.