Why the three initial tables? Why not just put everything into one? This is much easier answered if I could see what you're talking about. Upload some screenshots.

I need to use a button, (Combine All Accts) to execute a series of programs.  The functions work now individually but combining them does work.  Coping the SQL code for each operation does not work when they are combined.  I'm not a programmer.  Any directions on how to code the following operations you can give would be great.

1.Copy tblAllNZAccts to tblNZAcctsBU  (Copy all tblAllNZAccts old records into tblNZAcctsBU)
2.DeletetblAllNZAccts  (Delete all records in tblAllNZAccts)
3.AppendChkNZ1          (Appends all tblChkNZ1 Records to tblAllNZAccts)
4.AppendChkNZ2          (Appends all tblChkNZ2 Records to tblAllNZAccts)  
5.AppendChkNZ3         (Appends all tblChkNZ2 Records to tblAllNZAccts)
6.Open Report RptAllNZAccts

Have you created individual buttons for each operation?
Are these macros or via vba?

No have not put this in any buttons.

I just just individual Append Queries and Delete Query.

Not that I use Macros but you could create one and add each item one after another then run that macro with a button.

(You could then convert it to VBA with the button in the ribbon and see what's going on)