Pictures are never 'in' any particular program. They're simply 'on' your hard drive and, in your case, Picasa 3 is the program that you use to view them. So you can transfer them to a pen drive without involving Picasa 3 at all.
To do so, start by creating a folder on the pen drive to put them into. (It's not strictly necessary to create a folder; you could just put them straight onto the drive. However it helps to keep things neat and tidy): Plug the drive into a USB port on your computer. If a dialogue box opens, select 'Open folder to view files'. If you don't get a dialogue box, double-click on the icon for 'Computer'and then on the icon for your pen drive.
Either way, you'll now have a window open displaying the (empty) contents of the pen drive. Click on File > New > Folder and give your folder a name (such as 'Best Pics'). Then double-click on it to display its (empty) contents.
Now open a new window, showing the contents of wherever your pictures are stored (which might well be 'My Pictures). To copy a single picture across from that window to the folder you've just created simply click-&-drag it. To create a selection of pictures to be moved, click on each in turn while holding down Ctrl and then click-&-drag to move the whole selection across. To transfer ALL of the files, go to Edit > Select All and then click-&-drag everything.
ALTERNATIVELY:
Insert your pen drive into a USB port and create a new folder, as in Paragraph 2 above. Then open Picasa 3 to view your files. When you come to one you want to save onto your pen drive, go to File > Save As and navigate to the location of the new folder on your pen drive before clicking 'Save' (or 'OK'). Repeat as required.
IMPORTANT:
You should never simply pull the pen drive out of a USB port (unless your computer is turned off). You should first go to the 'Eject Hardware' button (at the bottom right of your screen) and 'eject' the drive. ('Eject' is a notional term here. It won't pop out of its own accord; you still need to pull it out but only after you get a mewssage telling you that it's safe to do so).