Changdeokgung is a UNESCO World Heritage site in Seoul, South Korea. It is often incorrectly referred to as Changdeokgung Palace. Palace in the name is redundant since gung means palace.
You can follow the instructions on the official website to reserve your ticket: http://eng.cdg.go.kr/reservation/reserv_01.htm
The process is in English, pretty straightforward to follow and you do not need a credit card to confirm the reservation. However, there is one detail lost in translation. That is, the reservation for a given month opens at 9am on the second Tuesday of the previous month. For example, the reservations for May 2016 opened on April 12, 2016. For the west coast (Pacific Daylight Time), this translates to 5pm on April 11, 2016.
The website seemed down around 6pm. When I looked around 9pm it was working (albeit slowly) and there were plenty of availability for May. In fact, all slots for English tours were available. The 2 tickets taken for the 2:30pm tour below are my reservations. There were no limitations on how many slots I could reserve, so I made reservations for three days in case we have bad weather on the first or second day.
For more details on Changdeokgung including the best time to go and other tips, watch out for future posts or my Seoul travel guide (ETA: Fall 2016).
Ray Ray's Guide 