How do you take an HDR photo when something in the photo is moving, like waves for example?

You can shoot the photo in RAW as opposed to JPG. You can then adjust the RAW photo into 3 separate exposures, (low, middle, & high), then use software to merge the 3 saved exposures of the same image.

You should be able to get 2 stops either way on the RAW exposure which should be plenty to do the job if you meter it correctly.

Here’s a flickr group for examples of that method:
http://www.flickr.com/groups/raw2hdr/

It works pretty well, but you are limited by the exposure range of your sensor. If you shoot print film you can get around 10–12 stops on your single exposure, about the range of a 3-shot HDR image. (If you don’t tone map it, it just looks like a wide exposure shot with details in shadows and highlights, the typical “harsh” HDR image is done by tone mapping to increase local contrast and flatten overall contrast), you get about the same exposure range if you shoot medium format digital, but I would guess that’s not an option for you.

Most of the HDR programs also let you mask areas of the image—if you only have one person (or some trees in the wind) and you don’t need 12 stops across the person, you can mask the image around them.

A lot depends on how much movement is taking place and how fast your shutter speed ends up being. If you have a fast shooting DSLR like the D300/D3 which can crank off 8 fps [with the battery pack] and you’re using autobracketing to shoot , say a 5 shot bracket. Then unless the individual shots are at a really show shutter speed, your effective shooting interval is about 6/10’s of a second. If the slowest shot is at 1/500 or so, the amount of movement may not matter, if it’s say slowly moving tree branches. That being said, you’ve hit on the fatal flaw of the HDR process.

I believe we’ll see new cameras appearing in the near future that will be able to shoot a lot of shots very, very quickly like the new Casio 60fps model announced at the PMA show. If they add an autobracket mode to that puppy, your problem may be solved, except for night shots.