Newbie question about extrusion of hemispheres I am trying to extrude a small section of a hemisphere into a flat surface (like the depressions in a Mancala board....or the death star main gun).  Correspondingly, I want to extrude a matching section outward in different flat surface to fit into that depression.

I have been scouring the web for tutorials, but not much has come up with adequate explanation for someone just beginning.  What is the correct/best way to do this?  I have seen some people make small extrusions, then scaling, then extruding, and scaling again (Repeatedly), but this seems a little....like a hack rather than a proper method to do what I'm looking to do.

Any help would be appreciated!
bottom left:
Create a sphere and a cube. 
Set a Boolean modifier on the cube.
Set the modifier's operation to "difference" and use the sphere for its object. 

bottom right:
this is the result

top left:
Subdivide a plane or mesh 2 times
Inset the 4 center faces
Extrude
You could at this point select the extrusion and hit alt shift s to spherize the center. Otherwise, just try to make the shape I showed up there by hitting shift+z while scaling the center most verts. 

top right:
this is a subdivide modifier applied to the top left mesh