A general note regarding windows in, erm, Windows!
If the window has been maximised you can't drag the edges (with the little arrows). You need to click on the 'Restore down' box first. (That's the one with overlapping rectangles, in the top right-hand corner, between the 'minimise' and 'close' boxes).
However there's no reason why you even need to have Picasa open at all. Your photos aren't 'in Picasa'. They're simply in a folder (or a collection of folders) on your PC, from where any program can access them. If you simply open the relevant folder (which is likely to be 'My Pictures' or a subfolder inside it) you can drag and drop files (or copy & paste them) to wherever you want.
Chris