This one seems to give problems, particularly for Mac users, so here's the procedure.
Windows is easy. You just right-click on the phone and import, specifying the thumb drive as the destination. Windows gives you the option to delete the imported photos from the phone.
The Mac is also easy IF you know where to go. That place is PREVIEW, not IPHOTO. Plug in your phone, open PREVIEW and select IMPORT FROM IPHONE from the FILE menu. You can then specify the destination, and decide whether to delete the photos from the phone.