I would imagine if you have two slots on your PC you could plug one into each. They'd come up as E drive and F drive or something. You could call both up on your screen side by side then drag and drop at your leisure (control+a will highlight them all and you can transfer the lot at once.)
Plug them both into a computer and copy the files across. If you can only plug one in at a time, then copy the files to a temporary location on the computer, and then copy them to the new stick.
However, if unfortunately you are limited to one socket,then you will have to do as is said by KristalB.... "copy the files to a temporary location on the computer, and then copy them to the new stick."......Or get a 'Doubler'