The most famous sections of the wall in Beijing are Badaling, Mutianyu, Jinshanling, and Simatai. You can get to these regions by taking bus line 877 or S2 train to Badaling directly. Bus 916 Express takes you to Mutianyu with a transfer at Huairou
Often, the bus signs are in Chinese, so we recommend downloading Google translate app or taking a picture of the place you want to go and asking your hotel receptionist to write down a written translation
A much simpler option is taking a private car, which costs around CNY 800-1,000 for a round-trip
There are plenty of tour companies that provide hassle free tours to and of the wall:
Bear in mind that the closer spots of the wall (Badaling, Mutianyu, Jinshanling) are popular, meaning it can get extremely busy. Therefore, think about visiting less populated spots, such as Huanghuacheng and Jinshanling. These still have amazing views, with only part-restored sections
Badaling, Mutianyu, Jinshanling and Simatai have cable cars
Take into consideration the complexity of the wall… it is a hike, so for those who have walking issues, the closer spots are more accessible
From Mutianyu you can get a toboggan down. Much easier on the old legs!