Astrophotography is truly an art, and something that challenges me. But shooting the Moon or Milky Way is really just a matter of exposing for light. Yes, it can get complicated, and very expensive if you want all the bells and whistles, or if you want to make a career out of astrophotography and sell your work in big fancy galleries.
But if you are like me, you can get lucky without any special photo equipment.
What I like about photographing the moon and stars is that it's often a matter of good guesswork as to the exposure and shutter speed, or ISO. I like trying new settings, and having to figure out timing, etc. There is no right or wrong way of photographing the night sky, although those specializing in Astrophotography have a unique understanding of equipment and other techniques that amaze us. But you really don't need to know that much, just some simple rules.
Note, the above photograph of the Blood Moon was taken at 8 p.m. Sept 27, 2015, ISO 2400, F5.6, 2 seconds open bulb with a 135mm lense without any software or other calculations. I shot this from my backyard in the city. I did not shoot RAW, I shot JPG because I was simply experimenting before my trip to Joshua Tree, California and wanted to test the optics and functionality of the Canon 70D. I set it on AF, but manually adjusted the focus ring while holding the shutter button down half way until I knew it was relatively sharp. A better image would have been one that showed the foreground in the scene… but I still think it worked for me.
Use a tripod. You must have a steady hand and learn how-to manipulate the manual settings in your camera. Using a shutter release cable helps keep vibration to a minimum, and lock up the mirror if possible. There is some slight star trailing effect in the image above, but that was ok for me.
The most recent Blood Moon, which won't happen again for 30 years, was a good example of simply locking down the camera on sticks, and randomly guessing the exposure, ISO and shutter speeds until it worked. Pulling focus was the most difficult thing about it.
I've read countless posts about calculations, etc. and I think it's all a bit silly. Making images is a matter of trial and error, not calculations because every camera is different and every person sees something different. The one thing that I suggest is to have an open mind, and enjoy the process. Tinker with exposure times, F stops and shutter speeds. Mess around with ISO settings too. If you practice enough you will ultimately get it right.
Enjoy the night sky!