If you have an atomic clock in your GPS device, you need to see 3 satellites to get a fix. As you said, you calculate travel time for the signal from the atomic

If you have an atomic clock in your GPS device, you need to see 3 satellites to get a fix. As you said, you calculate travel time for the signal from the atomic clock on the satellite to the one on the receiver and that puts you somewhere on the surface of a sphere. Two spheres intersect to give you a circle, and a third gives you a point (technically 2, but one is probably in space). Doing it like that would require you to have an atomic clock in every receiver though, which isn't feasible (and anything less accurate would make the fix too inaccurate). Instead you add one extra variable (current time) and one extra constraint (extra satellite) and the equation is solvable again. This is why you need 4 satellites for a fix. The solution to the equation not only gives location but also precise time, which is why GPS receivers can be used as standalone time references. The other thing you need to know to do all of this is where the satellites actually are: this information is called the ephemera and the almanac. You can download this from the satellite signal, but it is very low data rate and takes several minutes. This is why handheld GPS receivers can take time to get a fix. Mobile phones instead download this from the network which is why they can make very fast fixes - they just need to scan frequencies to get a lock while doing the download and then do a bit of maths.