How can I extrude a dome from a circular face? I have the following mesh:



I would like to extrude the face at the center so that a dome forms out of it, such that the dome's boundary would be exactly that of the circle. (Think bubble wrap.) 

Is there a quick and easy way to do this?
Yes, try extruding and scaling it multiple times:



To help make the extrusions more even, you might try using the To Sphere operator (&#9095; Alt&#8679; ShiftS). You can define where the center of the "sphere" To Sphere uses by using the 3D cursor as the pivot (.).

If you want to be more precise, try adding a sphere and deleting half, then using Bridge edge loops (W, E)



Note that the number of vertices on the perimeter of the sphere should match the number of vertices around the initial circle.