Moire patterns are interference lines or patterns that appear on scanned images from magazines or books that use halftone printing. Although some scanners offer "descreening" functions to remove the moire before you get the scanned image, the results are not always what you want. You can use several approaches in Photoshop to alleviate the moire problem, at least to an extent.
First, if your scanner does have a "descreen" option, turn it off because you will be handling it yourself in Photoshop. You don't want to use any of the following methods with the descreener on, since the result would be worse than just using the descreener alone.
Before you take your scanned image into Photoshop to remove or reduce the moire pattern, make sure that you have scanned it properly. Scan in the document at the highest resolution your scanner and computer can handle. You need to have it at least 300 dots per inch, and 600 is preferable.
With your image open in Photoshop, Select "Filter," then "Noise" and click "Despeckle." Then select "Image," then "Image Size"; in the dialogue box that opens, resample the image to half of whatever resolution and size you used. Make sure that you have changed the "Interpolation" to "Bicubic" and click "OK."
Resampling the image will blur it slightly, so go to "Filter," then "Blur" and select "Unsharp Mask." Despite the name, this filter is actually used to sharpen an image. Adjust the settings until you like the preview. Remember that too much can cause the object in the image to have a halo effect around it.
A different filter you can use to remove moire patterns is Gaussian Blur. This filter should not be used in concert with the previous method. Go to "Filter" and click "Gaussian Blur." Adjust the settings until you like the preview. Resample the image as before, and then use Unsharp Mask.