Physical image size is only one factor to consider when preparing images for the web. You must also take into account the actual size of the file; that is, how many bytes is your image? A good target to shoot for is a file less than 50 Kb. You can go higher, but keep in mind that your site is going to load slower the more that you put large files on it, including images. Any of your site visitors who use a dial-up connection will appreciate not waiting 5 minutes for your graphics-rich page to load.

Typically the smaller the image (in pixels) will yield as smaller file size (in bytes), so that if you're dealing with a small image you probably won't have to compress it.

In order to get your file size smaller, you will have to use a graphics editing program like Adobe Photoshop, Corel Draw or XNview. Again, each program differs in how file compression is achieved, but you can view this video on using Photoshop for image compression (the first half is about resizing).