Follow overhead signs inside the station for "Bus Transfer Hall"
Find bus 916 Express ("916快" in Chinese). Make sure to take the express bus as the normal version takes a long time.
916 Express costs 12 RMB and takes about 1-1.5 hours depending on traffic. Payment is by cash onboard the bus, or by Beijing transit card (i.e. Yikatong)
Bus runs between 5:50am and 7:50pm, once every 15-30 minutes
The last bus back to Beijing is at 6:50pm
Take bus 916 for 15 stations to Yangjiayuan (杨家园) Bus Station, located here in the city of Huairou north of Beijing
Get off at Yangjiayuan and walk 700 meters (south -> east -> north, like this) to Yujiayuan (于家园) Bus Station, located here. I know it's confusing but Yangjiayuan and Yujiayuan are two different stations
Get on bus H25 at Yujiayuan station. This bus costs 8RMB. Stay on this bus for 24 stations and get off at Xizhazi (西栅子) Station, located here. Should take about 1.5 hours.
There are only two H25 buses a day, at 11:30am and 4:30pm, so you need to leave Beijing by 9am the latest, even earlier is better to avoid unexpected delays
If you miss H25, you can also take a taxi from here to Xizhazi for about 120RMB-180RMB and 1 hour.
Unfortunately, the H25 bus from Xizhazi back to Yujiayuan also runs twice at day at 6am and 1:30pm. Therefore, there's no way you can catch the H25 back. Instead, you need to walk or taxi to Badaohe (八道河) Bus Station, 5km east of Xizhazi, located here, and then take bus H13 back to Yujiayuan (于家园) Bus Station. H13 is also limited each day, passing by Badaohe at around 5pm
The village of Xizhazi is surrounded by the Great Wall to the south and west for 20km. The most common starting point is Zhenbeilou (镇北楼) sometimes called Zhengbeilou (正北楼), a watchtower perched 1000m on top of a peak. You can get here by hiking south for about 1hour. There is a well trodden path you should be able to follow. Check with locals if you need directions.
From Zhenbeilou, hike east will be downhill and you will get to Mutianyu eventually. Hike west will be the bulk of Jiankou great wall and is much more steep and dangerous, but offering some very scenic spots
Here's a nice map of the Xizhazi village and Jiankou great wall made by Tour-Beijing. In the map below, "Team 2 Xizhazi Village" is where the H25 bus's Xizhazi bus stop is at. The red "Starting Point" is Zhenbeilou. Everything between Ox Horn Bridge and Beijing knot is considered Jiankou Great Wall
Via Mutianyu Great Wall
Mutianyu is a popular section of the Great Wall to the east of Jiankou. These two sections are connected
When you get to Mutianyu, keep hiking west along the wall for about 5km and you will get to Jiankou
If your goal is to visit Jiankou, this method is only doable if you plan to camp the nighton the wall. You don't have time to hike to Jiankou from Mutianyu and then get back in a single day