Photography is an important part of enjoying the Great Wall. It's good for a memory aid, as nobody can remember every detail. And it's good for sharing, because no description can do justice to the Great Wall. Actually, no photo can do justice to the Great Wall either, considering the two-dimensional limitations of photography, but pictures are much better than words in this regard.
Your photography activities on the Great Wall are going to be a compromise. At one end of the spectrum, you could skip taking photos entirely and just enjoy the experience. At the other end, you could constantly take pictures, recording almost everything and paying more attention to photography than to walking the Great Wall. You will have to find a happy medium between these two extremes. This will be different for different people. Many people come to the Great Wall with photography as one of their primary goals. These people will want to choose locations that offer the best photo opportunities, and they will want to take thousands of photos. Others will see the camera as a burden that they must accept in order to have some photos to take home. Most people fall somewhere in between, and for these people, often they make the mistake of taking too few photos. In order to avoid this mistake, you should try to make photography as effortless as possible. Bring a camera that's small, lightweight, and easy to use, yet takes high-quality photos. Find a way to carry your camera so that it's easily accessible. Access is very important. If you have to dig your camera out of a bag, and especially if that bag is on your back, you will take too few photos, and the frequency of your photography will probably become less and less as your walk progresses. Also be sure to carry plenty of memory capacity and spare batteries so you won't need to worry about how many photos you can take.
Photographing the Great Wall is irresistible to most people. The incredible sight of the Great Wall winding its way over the terrain just seems to beg to be photographed. Enjoy taking these photos, but don't forget to include variety and detail in your photos. Take close-up photos of the interesting details of the Great Wall. Try photographing from unusual angles. Shoot from high and low instead of eye level. Look over the edge of the Great Wall and shoot from there. Get off of the wall and shoot from a distance instead of taking all of your shots from the top of the wall. Photograph other members of your hiking party, both in posed shots and in candid shots. They will appreciate these photos very much when you present them.
Keep in mind that, in person, the steep and dramatic layout of the Great Wall can be very impressive indeed, but that photos often can't convey the extremity of the terrain. Try adjusting your perspective in order to best capture the three-dimensional aspects of the Great Wall. If you're using video, be sure to pan not only horizontally but vertically as well in order to relate the feeling of height and steepness.
Once your Great Wall experience is over, make an effort to share your photos. Everyone's photos are different, and there are always people who will appreciate and enjoy yours. Obviously the Internet is the ideal place to share your photos with the greatest potential audience. You can share your photos on forums and you can share them on geographical mapping sites such as Panoramio that will allow people examining specific locations to see your photos from that area.
If your primary goal at the Great Wall is photography, your approach is going to be different. Naturally, you will want to take photos in clear weather which, especially in the east, where the population is greater, may seem elusive. There is a lot of smog in China and often there can be rain in the mountains, since they are essentially the southernmost mountains reached at the northern edge of a plain. The best way to find the clear weather you need for photography is to go to the Great Wall in mid-September or later in the year. Then you will need to wait for clear skies and wind from the north. Winter provides the best possibility of clear skies, if you can tolerate the cold. These conditions combined will give you the clearest air and the best photos regardless of the time of day.