I'm assuming that you're referring to the Picasa software on your computer, not to the 'Picasaweb' website .
Pictures on your computer are never 'on' or 'in' any particular program. They're simply stored somewhere on the hard drive, from where they can be accessed by ANY suitable program. (The fact that Picasa is you default image handling program is irrelevant).
I'll assume that your pictures are in your 'My Pictures' folder (which is the most likely place). I'll also assume that you already know how to connect and access your external hard drive. (If not, please post again).
Click on Start > Documents > My Documents (NOT 'My Pictures'). Look for the 'My Pictures' folder. Right-click on it and select 'Copy'. Open a window displaying the contents of your external drive. Right-click and select 'Paste'. Job done.
Chris