Changdeokgung is closed on Mondays so you can visit the palace on any Thursday you like. The admission fee for general tour except Biwon, or Secret Garden, is 3,000 won for adults, and you need to pay extra 5,000 won for the rear garden.
As you are well aware, Biwon can be accessed only by guided tour. English interpretation is provdied twice a day on 11:30 and 15:30.
You can find more information about the palace and tour at http://eng.cdg.go.kr.