Can't Separate Objects

When I add a second object it is linked to the starting cube. I can deselect all but cannot select one to be edited separately. I have tried shfting to object mode and right clicking on one of the objects but when I try to move it both objects move together. What have I done wrong?

I’m a rank beginner using 2.46 on Debian Lenny (stable). I have learned a bit about moving and editing an object (Page 61 of Blender for Dummies).

Sounds like you added the second object in Edit mode. They are effectively a single object. To avoid this add other objects in Object Mode.