First, reformat the drive to Mac OS Extended. It sounds like it's formatted for MS-DOS. To reformat the drive you need to do the following:
1. Open Disk Utility in the Utilities folder of your Applications folder.
2. After DU loads select your hard drive (this is the entry with the mfgr.'s ID and size) from the left side list. Click on the Partition tab in the DU main window.
3. Set the number of partitions from the dropdown menu (use 1 partition unless you wish to make more.) Set the format type to Mac OS Extended (Journaled, if supported.) Click on the Partition button and wait until the volume(s) mount on the Desktop.
4. Select the volume you just created (this is the sub-entry under the drive entry) from the left side list. Click on the Erase tab in the DU main window.
5. Set the format type to Mac OS Extended (Journaled, if supported.) Click on the Options button, check the button for Zero Data and click on OK to return to the Erase window.
6. Click on the Erase button. The format process will take 30 minutes to an hour or more depending upon the drive size.
I would not recommend backing up by drag and drop. Although this may work fine for you personal files it will not work to back up system files. Instead I recommend you use a backup utility that can create and maintain bootable clones of you main hard drive. If you portable drive is a Firewire drive then a bootable clone on the drive could be used to boot your computer in an emergency. If the portable drive is a USB drive it cannot be used to boot the computer, but maintaining a bootable clone will make restoring your main hard drive simpler.
Appropriate software to consider includes Carbon Copy Cloner, SuperDuper!, Deja Vu, Retrospect Desktop, Synchronize! Pro X, LaCie SilverKeeper, etc. All can be found at www.versiontracker.com.
