Digital cameras these days have gotten pretty good at producing noise free images. Most modern DSLR's can produce images with almost no noise at ISO speeds up to 400. Sometimes however, shooting conditions make using such ISO speeds impossible. In other cases there may be areas of an image that are sufficiently underexposed to produce an increase in visible noise. In either case you may wish to remove some of that noise to produce a cleaner and more appealing final product.
Removing Noise from the Entire Image:
If you shoot RAW (and I suggest that you should) then whichever RAW conversion software you use will have an option for noise removal. These programs generally do a pretty good job at removing small amounts of noise. The catch however is that they have to be used in extreme moderation. If you overdo the noise removal at this stage you will be degrading the overall quality of the final image. It seems that most noise removal software is essentially selecting and blurring noisy areas. This may be fine for a solid background but is probably not what you want to happen to that tack sharp image you just worked so hard to create. When it comes to removing noise from the entire image the general rule of thumb is "less is more".
Selective Noise Removal:
After you have converted your RAW image ther may still be undesirable amounts of noise surrounding the main subject of your photo. Noise tends to show up more prevelantly on solid background colors or smooth areas of water. Fortunately, since these areas generally don't have any details to preserve you can further remove noise from them without degrading the quality of your main subject. Here's how...
The first step is to select the parts of the image that you do not want to remove noise from. In this case the duck. To do this I generally use the magic wand tool from the toolbar (see also article on making selections).
You can fine tune your selection by using "Refine Edge" dialogue box.
At this point you can selectively remove noise from the image. To do this use the noise removal filter (Filter > Noise > Reduce Noise). Because you are working on a smooth surface with few or no details you can apply the noise removal filter at a high strength (I usually use 9 or 10).
And that's all there is to it! A quick technique to remove that distracting noise from images and one more way to make your final product that much better.
One final thought to consider is that while you have the backgrond area appropriately selected you may also want to make subtle adjustments to the color or saturation. For example in this image I would slightly tweak the color of the water to make it a little bit lighter and a little bit more blue.
The Final Product: