It is a simple process, but not necessarily obvious.
On the Shared Documents page, click the arrow next to "Actions" and select "Open with Windows Explorer". This will open up a Windows Explorer window and allow you full options to copy, paste, add, delete as needed, even though the subtitle indicates it is only for adding files in.
For Sharepoint 2010 users, Go to Shared Documents Page, Click on Library tools->Library, Connect and Export Ribbon ( it is in the middle of the ribbon bar) and select the "Open with Windows Explorer".