How to copy files between your local computer and one connected through Remote Desktop

You can't drag and drop files, but you can copy and past files and folders.

From Microsoft (http://support.microsoft.com/kb/313292):

To view the disk drives and files for the redirected disk drive.  From your local machine.
1. Click Start, point to All Programs (or Programs), point to Accessories, point to Communications, and then click Remote Desktop Connection.  Or if you don't see the option, click Start->Run-> and type in mstsc.exe and hit enter.
2. Click Options, and then click the Local Resources tab.
3. Click Disk Drives, and then click Connect.  Or, click the More button and then check the Drives checkbox.