Install Wine as specified in this blog; Then type winecfg in your console and you will see a GUI popping up. Ensure that your Windows Version in the Applications tab is Windows XP. Download Picasa and double click the exe it should start the installer in the Wine emulator; if not use the following command -
Now proceed with the installation as you would in Windows. If you choose to have a desktop shortcut you will see one in your desktop double clicking it would start picasa in your wine emulator. You can also start Picasa from your Applications -> Wine -> Programs -> Picasa2 -> Picasa2; you will also find the uninstall action there (which I did not use).
Now you can enjoy using Picasa on your Ubuntu; Happy Image Sharing!