Now select the bottom sphere and go into edit mode (tab).  Select all vertices and then go to the "link and materials" panel in the edit buttons.  On the left side of the panel it says "Vertex Groups".  Click on the "New" button directly below that label to create a new group.  Two new boxes pop up.  The top one should say something like "Group".  Click in there and change the name of the group to the name of the bottom bone, which you looked up before.  The name is probably "Bone", so call your group "Bone".

Underneath that box is a box for the weight of the group.  In this case we will want it to be 1, on other cases where you want the bone to deform the mesh you might want some other value or you might need to use weight paint mode.  Don't worry about that right now, just make sure it says 1.

Make sure all your vertices are selected, then hit the Assign button.

Leave edit mode and do exactly the same thing for the small middle sphere.  These two objects will now follow the bottom bone when you move or rotate it in pose mode (more on that later).

The top sphere is set up almost exactly the same, except we want it to follow the top bone instead of the bottom one.  Do everything the same, except when you change the name of the group, change it to "Bone.001" (the name of the top bone) instead of "Bone".