I've only been to the Great Wall in Beijing, which is a huge segment of the wall.
It would be fantastic if the Great Wall were just a single, fully connected really long and thin park. Unfortunately, this is not the case. There are instead a bunch (dozens?) of segments that are beautifully reconstructed, like in your picture. These are run as tourist attractions/natural parks by the governments, and are great for day trips. Generally, these well-built areas will have a definite starting and stopping point, and security guards.
Other parts will have never been maintained, and are also very interesting. Sometimes of these non-rebuilt areas are also organized as a tourist attractions, sometimes they are not. These are highly recommenced, if you have time. My favorite segment ran through the middle of a sheep farming village, and required that I walk through a small river. Very beautiful. I have seen camping there too.
Other parts are on private property and will not be accessible. I am very curious about the article in the answer by @chx; it would be great if there were detailed notes available.