How does the GPS scale and deal with potentially millions of requests per second and respond in real time?
If someone stands on a hilltop over a large town and screams "the Mongols are coming!" then everybody knows what's up and they get out of town. The lookout doesn't have to say "Hey Timmy: The Mongols are coming! Hey John: The Mongols are coming! Hey Sarah..."

GPS is just a bunch of satellites in orbit screaming "I'm over here!" in radio frequency. A GPS receiver just tries to make out the different satellites screaming their positions and does the number crunching for "If satellite 1 is over there, and satellite 2 is over THERE, and satellite 3 is just about in THAT spot... then I must be around HERE someplace".

Technically, the receiver is listening for each GPS satellite's timestamp and orbital position. It calculates the time the different satellites' signals took to reach the receiver, which gives the receiver the distance from each satellite. Given the distance to each satellite, you know your own position.

How? Imagine three satellites in orbit and you on the earth, with long sticks in between. Those sticks are only going to meet in one spot.  With one satellite and one fixed length stick, you could be anywhere on a sphere around the satellite. With two satellites, you could be anywhere on a circle centered between the two satellites. With three satellites, your position generally can only be in one spot. Usually, four satellites are required for any precision, though. (The calculation of distance from the satellites is usually not that precise, so knowing the distance to more satellites is better)