It looks like you'll need to create a series of spherical surfaces (like an onion has layers).
Next, start simple, and from a standard reference plane, extrude a symbol up to one of the "onion skin" surfaces.
Repeat a few times to get the process down, but change the surface you extrude up to so you get different depths.
Next, start creating new reference planes to start your sketches on.
Quickly you'll discover that this is going to be rather time consuming and repetitive.
You could try doing all this as an assembly, and arranging, and then cutting away portions of the parts, or even starting with parts that match the curvature of the sphere you want, but in the end it will still take a long time to try and position all of those letters correctly.
I hope someone has an idea to speed the process up.
Chances are that the reference image was not created in a CAD program like SolidWorks though. Maybe in a program like Studio Max (as an example), that is a very easy task?