We all get twitchy when we have to wait for web pages to download. Graphics are usually the biggest elements in file size so be sparing with them and keep them skinny!
Two common file compression schemes for graphics are GIF and JPEG. Image-editing programs should have the option of saving in these formats but, if you don't have that option, check for shareware programs online that you can download. Some ideas of where to look are on the Resources page.
Typically GIF works best with small graphics and JPEG with photos - but not always!
GIF depends on reducing the color palette of a given image to the smallest number of colors. You can control how many colors are used and decide how much you can reduce them and still get a good image. Because you are limiting the palette, GIFs start to look dithered quickly. This isn't a problem with single-color square graphics.