Depends
If yoou only want copies of your pictures ten export to the external drive (see the user tip on exporting for details on the options available)
If you want a backup for your iPhoto library it is buest to use ongoing, constant backup software like Time Machine
If you want a one shot copy of your iPhoto library then
Moving the iPhoto library is safe and simple - quit iPhoto and drag the iPhoto library intact as a single entity to the external drive - depress the option key and launch iPhoto using the "select library" option to point to the new location on the external drive - fully test it and thenrepeat to switch back to the main libary
And be sure that the External drive is formatted Mac OS extended (journaled) (iPhoto does not work with drives with other formats) and that it is always available prior to launching iPhoto
And backup soon and often - having your iPhoto library on an external drive is not a backup and if you are using Time Machine you need to check and be sure that TM is backing up your external drive
LN