On a clear (cloudless) night, you can get some excellent shots of the moon. Having some form of zoom lens definitely helps. Generally it will look better with something 300mm or better. However not everyone has a lens like that hanging around.
Everyone has different “recipes” on how they photograph. Because of the magic triangle (ISO, Shutter Speed, Aperture), this can vary depending on ambient lighting, lens being used, etc.
I ended up using a 2x extender on a 400mm lens getting a nice effective reach of 800mm. I locked my ISO to 100 (can lock up to 400 or even 800). I set my DSLR into “Tv mode” so I could adjust my shutter speed. I ended up finding 1/60 to 1/100 sec being ideal due to the bright light of the moon on this particular cloudless night. This resulted in an F-stop (Aperture size) of f/11 (which didn’t really matter to me, it is the variable part of the triangle for my intended purposes though f5.6 is good if you want to lock this). For more info on the magic triangle, check out BetterPhoto or JaneGoodrich.
Focusing can be a challenge. A very helpful way to achieve it is DLSR’s which support Live View shooting with zoom. On my Canon I would go live view, move the view to the right edge of the moon (to see the detail of the craters for this example), and zoom in 10x (which my Canon allows). Ensure your lens is set to manual focus. Turn off your image stabilizer if present on your lens. You MUST be using a tripod for this. There is no hand holding for almost every dark/night/evening shot. You can then tweak your focus manually until it looks crisp for the details on the craters. Use a very inexpensive remote shutter control for your camera to take the shots. That way the camera can sit perfectly still on the tripod. Camera shake will cause blur for exposures like this.
Take the photo, go to view it, zoom in to some detailed section, and ensure it looks good. Then play with the shutter speed (Tv mode) until you get something that looks great for the exposure.
I am not an artsy person. My brain works on the technical side. I love applying photography to different situations (such as this) to technically figure out how to do it. It is a personal challenge for me. Other people look at it and say “Oh, another photo of the moon” however I can say “I took that photo and it feels great knowing that”.
Photo of moon I took on my Canon DSLR: