What is the correct way to remove a FireWire or USB drive from your system?

If you're using a Mac and removing a FireWire or USB drive while your Mac is still booted, drag the icon of the drive to the trash. This will spin the drive down, and correctly dismount it from the computer. If you're using a Windows, do the same thing by clicking on the Safely Remove Hardware button in the bottom right task bar, and choose the drive from the list that appears.