Ground Wire Installation
To meet current NEC codes you cannot have neutral and ground share the same grounding rod.  Ground requires its own separate rod from each panel and sub-panel installed in the house.

The depth of the rod outside depends heavily on your area as factors like precipitation, soil composition and climate affect just how far the rod needs to be placed into the ground.  Performing this work likely requires that you obtain a permit from your local municipality, meaning that you will need to have an inspection anyway.  I would ask the inspector what he will be looking for in a ground rod.