In DW, you would go to Site > New Site and create a new empty site with just your ftp username, password and directory. You would then open that site in DW and choose the Get button from the Files tab to download the site onto your computer. Then you can make any changes you like to any page and upload them.
There may be some oddities in Design View because it's likely that the site uses some proprietary code that DW itself won't render correctly. Preview In Browser to make sure the pages look the way you want before uploading.