I want to dispel a frequently misunderstood concept here- the moon does not move nearly as fast as most people think!
The true rate of movement of the celestial sphere (the stars) at declination zero across a 12mpx DX sensor is 1.3634 pixels per second per 100mm of focal length. The moon actually moves about 3% slower (approximately 1/29.5 slower than the stars). The moon moves fastest at declination zero and varies +/- about 27 degrees, so it moves even slower at or near the extremes but the effect is so minor that we can ignore it for our purposes.
That means that the moon moves 2.6 pixels per second with a 200mm lens. That's not very fast and it implies you could shoot the moon at as slow as about 1/2s at 200mm and get only one pixel of blur.
With a 1000mm lens, it implies a movement of 13.3 pixels per second. That implies that a 1/15s exposure will yield about 1 pixel of blur, and a 1/30s exposure about 1/2 pixel of blur. As proof I offer this image:
The image was shot at 47 degrees altitude, not ideal but about as good as it gets for that phase of the moon, at declination 26d 47m. It was shot 3 minutes after the start of nautical twilight, about 56 minutes before sunrise.
That image was part of a series of 11 out of 12 days straight (days 16-27 of that lunation) I shot starting Aug 29, 2007. To get 11 of 12 days of clear skies was a miracle that may never be repeated . If I had known I would have such a run I could have gotten the 12th day (lunar day #18 - the 2nd day of the series), which was partly cloudy but with patience could have been shot. But whodathunk?
I can tell you that the above was not a fluke. Over the years I've spent a bit of time verifying the edge of this envelope and adopted 1/30s for 1000mm as my own limit for ideal results. Some of the later dimmer crescents in that series were shot as slow as 1/6s at 500mm with very good results, the seeing being a far bigger issue at the necessarily lower altitudes.
All 11 images (plus the replacement for lunation day 18) are posted to my Phases of the Moon gallery:
All this is irrelevant unless you have a very sturdy tripod and head, in my case an alloy Series 4 Gitzo G1410 and a Markins M20 ballhead. If you get blur it is important to understand why, and it is likely your support or technique, not the turtle's pace of the moon
If your fuzzy moon is not due to it's movement, the next thing to check is focus. For lunar imaging LiveView is the best thing since sliced bread. I wish I had had a D300 (with LV) when I did that series (all with an MF lens working 500-1000mm and up to F/8 wide open). If your camera supports LivevView but you thought that was just another gimmick, try it (in tripod mode) the next time you shoot the moon!
Some blame "seeing" for fuzzy lunar images. In my own very humble opinion, I doubt that "seeing" (atmospheric issues) is a big deal when the moon is over 40 degrees altitude or so- at 200mm. Unless you have very bad seeing and that is usually accompanied by high winds. I say this based on over 100 evenings of lunar imaging I've done at far higher focal lengths. It matters at 1000mm, likely not much at 200. I rarely see good seeing. Shooting it just over the horizon is a different matter - shoot the moon when it is high, at least 40 degrees elevation whenever possible.
If focus is good but your moon is still fuzzy and you have a good tripod, rethink your technique. If your camera has full mirror up (D300, D200, D2 series, D3) then use it, and count 5 seconds between mirror up and firing the shutter. If your camera only has "exposure delay mode" then try that, but be aware that the built in 0.4s to 1.0s delay may not be enough, depending on the length and weight of the lens and your support. If you don't have mirror up, try Long Lens Technique and shoot a lot of images. Using a remote without delay, hands off, at over 200mm will almost always result in some mirror slap blur. With my longer lenses (500/4 and 300/2.8) I can often get a better image with LLT than with the remote without any mirror delay.
There are seasons for each phase of the moon when it is highest in the sky. Right now October) the 3rd quarter is best but has to be shot at dawn as was the image below (tonight's moon and that image are both 24 day old moons). The first quarter is worst now, and best in the spring around March. The full moon is best in winter. Crescents are more complicated because of their low altitude and don't quite conform to the basic "seasonal schedule" but are best shot generally in the spring for the new moon and after the summer equinox for the old moon. If you live in Australia (anywhere in the southern hemisphere) reverse all that .
If you are shooting the starry background you can use the same formula (1.3 pixels/second/100mm) as the fastest rate the stars move. As you approach the celestial poles (North star in the Northern Hemisphere) the rate slows but that is a subject in itself. Just use this formula unless you have a set of tables and understand celestial coordinates. These exposures are necessarily long. You will find that for small enlargements and web page use that you can get away with several pixels of blur before the trailing becomes blatantly obvious.
<img src="https://images.nikonians.org/galleries/data/20685/Moon_24d_10h_90437.jpg" width="500" height="500" />