you upload your files using any ftp client and the settings provided by your ISP. Normaly your ISP recommends one, I suppose the most popular are cutetfp, wsftp etc etc. There are loads of free one out there.
DW had a built in FTP client which is perhaps a bit flakey. You setup the connections details in your site definitions and then in the site file panel you will see a double arrow button with flyout that says syncronise. Press that and it should syncronise your remote and local folders.
If you use the syncronise button only changed files will be uploaded.