Typically, you can do this with the file manager (which may have different names depending upon the distribution and window manger you're using; e.g., KDE, GNOME, Xfce or whatever). Open the menu (usually at the lower left corner of the screen and look for "file manager").
Both devices must be mounted. If you can "see" the flash drive content in the file manager and "see" the disk drive in the file manager you can simply drag and drop.
It's also typical that when you connect a flash drive or an external hard drive that it will auto mount and the content will appear in the file manager. If that's not happening, you'll need to mount one or both, depending.
It would be useful to have a little more information -- like what distribution, what window manager, does either or both drives auto mount when you connect them.
Hope this helps some.