This tutorial assumes that you don't have wine installed or you are using it in 32bit mode without any default libraries modifications.
Run this in a terminal window:
$ cd ~/Downloads
$ sudo apt-get install wine1.5 winetricks
$ WINEARCH=win32 winecfg
$ WINEARCH=win32 winetricks -q ie7
$ wget http://dl.google.com/picasa/picasa39-setup.exe
$ wine picasa39-setup.exe
After running Picasa setup, exit and from Unity Dash search "Picasa" and launch it from there. If you would like than drag that icon on your desktop and then you should set "Allow executing file as program" permission (right click on icon, properties, permissions).
That it! Simple.