I've talked to a lot of digital photographers who are disappointed with basic photo editing tools because they don't always have the intended effect. Take sharpening tools, for example: Somewhat counter intuitively, sharpening doesn't sharpen blurry pictures. But you can increase your subject's apparent sharpness by blurring everything else. This is also an awesome trick for adding a sense of depth to your photos.
Aperture and depth of field
Using a wide aperture (which equates to a low f-number on your camera's aperture dial) is a time honoured trick for blurring the background and forcing the viewer's eye to look at the subject. It also adds a sense of drama to an otherwise nondescript scene. You can get this effect when you take the picture by shooting in Aperture Priority mode and choosing a relatively small f-number.
If you don't remember to do that when you take the picture, though, all is not lost. Consider a photo like this one, in which the foreground and background are all more or less in the focus zone.
We can give the subject more impact by separating it from the background with the application of a deeper depth of field. To do that, open the image file in your favorite photo editing program. I'll use Adobe Photoshop Elements to describe the specific steps, but this is easy to do in any program that supports multiple layers.
Blurring your photo with layers
In the Layer menu, choose Duplicate Layer, and then click OK. This command does exactly what it sounds like: It copies the photo on top of itself as a second layer. You can see that in the Layer Palette on the right side of the screen.
Now that we have two identical copies of the photo open, let's add some blur to the top layer. Make sure the top layer is selected in the Layer Palette, it's probably called "Background copy."