What is the best way to photograph the moon with a digital camera?

You will need a tripod as long exposure is involved with photographing the moon. You will also need a fairly long lens - the moon, particularly on the horizon looks larger than it actually is, the camera lens is not fooled by this and the part of the image taken up by the moon will be quite small even with a longish lens (around 200mm say).

Assuming you've armed yourself with a tripod and a telephoto lens, then the other problem is exposure. At night, the moon is, effectively a bright blob in a large area of black. The camera exposure system assumes you are photographing an average gray scene (by average, I mean 18% gray). The result is that if you use the camera exposure system set to automatic, the moon will be very over exposed - perhaps by 3 or 4 stops.

There are a number of ways around this:

1. With an ISO setting of 100, the correct exposure is around 1/90 at F16. Set your camera to manual exposure and use that setting. If the ISO doesn't go down that low then you will need to adjust the aperture or exposure time appropriately.
2. Use a spot exposure facility (if your camera has that) and expose on just the moon.
3. Use exposure compensation and take the exposure down by 3 stops.

Between shots, look at the preview screen on the back of the camera and see what the image looks like - making adjustments as appropriate.

Although it doesn't look like it, the moon is moving quite quickly across the sky and you'll need to adjust the tripod regularly to keep the image in the viewfinder.

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