Think of the moon as what it is - you're pretty much seeing daytime on the moon - which would be similar to a bright afternoon day here on earth. So when shooting the moon itself, in order to properly expose it you need to use daytime exposures...same aperture and shutter you would use standing on a sunny beach of sand. As you might guess, that makes shooting night scenes with the moon in them very hard in one exposure - because to expose the moon properly, everything else in the shot would be massively underexposed. To expose the surroundings properly, the moon gets blown out badly. Most folks will try blending two exposures or more together, so that one is exposed for the moon and the other(s) for the landscape, then blend those exposures together in an HDR (high dynamic range) stacking software. But if you go to the extreme, and expose the moon with all its detail in perfect daylight exposure, and stick it against a long exposure night landscape, it often won't look very realistic. Ironically, it may be closer to what the eye actually saw, but your brain also tells you that the photo of a perfectly exposed moon against a night scene is photoshopped. For example, this was about what my eye saw:
But I had to use two shots and layer them in order to get it because the moon, even with the landscape being daylight, was still blowing out badly. It looks like I saw, but it also looks fake.
Sometimes, something in between the full blown out moon, and the fake-looking layered in moon, might be the best compromise - something that looks realistic in a photo, showing the moon a bit blown out, but properly exposing the landscape...to avoid letting the moon become TOO blown out, use the same HDR technique to take two or more exposures, but be gentle on the processing, and don't shoot as many stops between the exposures. By shooting two exposures 2-stops apart, I was able to get a good exposure on the foreground night landscape, and get a fairly well exposed sky with a blown out moon - but it's not as badly blown out as it would have been in 1 exposure - you can still get the idea that it's a moon, and it's not dominating the whole sky:
The other trick is to shoot right around sunset - even the hour or so before, with an early moon rise. It's about the perfect time to get a single exposure in which you can expose both the moon and the surrounding landscape just about perfectly together. By UNDERexposing a touch, you can get the moon exposure just right, while the landscape will be slightly darker than the eye saw, it can look quite natural - you essentially end up making a brighter daylight scene look like a natural dusk sky. I snapped this quick shot handheld - it's also a big crop - when I noticed this ship sailing out to sea under the rising full moon:
Hope that gives some ideas!
Sony DSLR-A68 / Sony 18-250mm / Minolta 50mm F1.7 / Tamron 150-600mm / Minolta 300mm F4 APO
Sony A6300 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / FE70-200mm F4 G OSS / FE70-300mm F4.5-5.6 G OSS / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses