Those appear to be english walnuts, or Juglans Regia as opposed to
native walnuts like Juglians Nigra or black walnut.
Here in California one rarely sees english walnuts that are not grafted to Juglans california as rootstock commercially.
They grow as weeks here, I have to pull them up all the time so I would say plant it 4 to 5 inches deep and in moist soil and leave them alone?