Well, the basic issue is that when you move files to another folder you are breaking the internal links to them.
Go ahead and get Dreamweaver operating. Once you do, go to the box to the right that says Files. You should find a link around there for Define A Site or Manage Sites. Go through the little "wizard" and tell Dreamweaver where your site is located on your computer, including pointing it to the index file at the Site Map Layout tab (which is in the wizard).
From then on you'll be able to drag and drop files within Dreamweaver's file manager and it will auto update the internal links for you.
Also, in the "wizard" is a place to set up FTP straight from Dreamweaver, so you can make changes and then "Put" them to your server directly from the Dreamweaver interface.
You would be STRONGLY advised to get yourself a Dreamweaver For Dummies book... it will help you a LOT.
"Whenever you find yourself on the side of the majority, it's time to pause and reflect." - Mark Twain