a folder for images in the site - FP creates one by default. Drag all your images ito this folder - FP 2003 will automatically update all the links on your site, so that the images display properly. Inside the images folder you can create sub-directories if you like, so that you can manage the images better.
If you find that over time you have replaced images with new ones, it's good practice to delete those that are no longer displayed, otherwise you can end up with dozens of image files that are simply sitting there doing nothing.
Normally it's not necessary to create folders for your html files - they can stay where they are. Once you've tidied up your images you'll find that things look a lot better, and you can upload the whole site again. That will bring the server version of the site into line with the version you have saved on your hard drive.