I had problems getting this to work with the instructions provided by google here. The beta version of Picasa includes a really nice feature where you can select images and easily synchronize or send them to you online Picasa library.

I found instructions here that works!  The instructions goes like this:

1. Open your /etc/apt/sources.list file with gedit:
$ sudo gedit /etc/apt/sources.list

2. Add the following line and save file:
deb http://dl.google.com/linux/deb/ stable non-free

3. Download GPG key from here, save it to your home directory and run this command:
$ sudo apt-key add linux_signing_key.pub

4. Install Picasa through your Synaptics Package Manager