With one measuring point and it's distance to a fixed target, you know that the target lies somewhere on the surface of a sphere with a radius equal to the distance.

With a second measuring point and it's distance to the same fixed target you can overlap those two spheres. Two spheres that overlap do so as a circle. You now know the target lies somewhere on the circumference of the circle.

With a third measuring point and it's distance, it's sphere will intersect the circle at precisely two points. This is the minimum required for GPS as it can usually discard one of the points using other knowledge (your receiver is not in space).

With a fourth measuring location the ambiguity is removed and you're left with a single location.

The orientation and location of the spheres don't matter as long as you know the precise locations of the measuring points, all measurements are taken while the target is fixed (which is why time synchronization matters here), and all the spheres overlap (in the real world noise, and mulitpath reflections make this quite difficult).

Source: I worked on wireless trilateration for several years for a commercial project.