Resizing images can be confusing because there are two ways of talking about the size of images: Pixels dimensions, and Print dimensions.
Pixel dimension is pretty basic, this is the number of pixels that compose your image. The more pixels, the more details and so forth. This is technically different than "Resolution" because resolution is pixels per inch (PPI), which as you can see involves inches which is print dimensions.
Print dimension is the size that the image will be when printed. This dimension is usually measured in inches or centimeters, NOT in pixels. This dimension is independed of the pixels dimensions, but one of the factors which creates the "resolution".
Photoshop Elements give you to ability to change the print dimensions and the pixel dimensions of your image. When you change the print dimensions, and decide to make your image 10 inches wide instead of 5 inches wide, you're simply telling photoshop to adjust it's sense of how big the image should be printed...this has no actual effect on the image; on the pixels. Changing the pixel dimensions (or ReSampling) is a different story. When you change the pixel dimensions of an image, you're changing the makup of the image. For instance, if you have an image that is 1000 pixels wide, and you want to "re-sample" the image to 2000 pixels wide, Photoshop just simply duplicates every pixel and it doubles the size. If you're going the other way, Photoshop simply drops every other pixel and leaves you with an image with half the pixels you had.
The important thing to know about resampling is that when you increase the pixel dimensions (re-sampling up), you end up with an image that has more pixels, but the same about of "details" that was in your original. This means that your spreading thin all the details that were in the original, and this generally results in a fuzzy, poor quality image. For more information on this, see page 305 in the book.
The very next step after opening a photo is often to resize it to an appropriate size for your final result. This idea becomes clear when you consider that images designed for the web get displayed at 72 ppi, and images designed for a printed publication get saved at 300+ ppi. Therefore, it is important to consider the use and final size of your project before you begin to edit your images.
To resize an image in Photoshop, choose Image>Image Size
Notice that the two check marked boxes just above this sentence are checked and mean that when you change any value, it will change the other dimension so to preserve the shape or "proportions" of your image. Also, since the Resample Image box is checked, you have the ability to change the actual number of pixels in your image. Otherwise, you can only change the Document Size or Print Size and changing values will only change the resolution and dimensions, not the actual number of pixels.
To resample an image (as mentioned above) means to adjust the actual number of pixels that make up a digital image. To resample down means to make the number of pixels that make up the image (and consequently the file size) smaller. This can be necessary, for instance, when you want to resize an image for a web site. The resample up means to increase the number of pixels in your image (and your file size). It is important to remember that resampling up will increase your total number of pixels, but it cannot create any more details that were present in the original image. Therefore, it is not recommended that you resample up, because the quality can only get worse. If you need a larger image with more detail, you will simply have to re-scan your image at a higher input resolution.