Walk 300 yards west and then north (like this) to the stop for bus H21, located at this spot on Kaifang Road (开放路). Make sure you're on the western side of Kaifang Road
Take bus H21 to its final stop at Xishuiyu (西水峪). First bus is at 5:35am and last bus is at 6:20pm. The bus should take 40min-1hour depending on traffic. Fare is 9RMB and you can pay with your Beijing transit card
Walk north for about 300 yards to get to the entrance to Huanghuacheng. You can also just follow the signs from this point on as it's inside the park area
The last H21 back to Huairou departs from Xishuiyu at 7:05pm. The last 916 Express back to Beijing from Huairou is at 6:50pm. So realistically you need to leave Huanghuacheng at around 5pm to make it back to Beijing.