Posted below are the exact commands I used to download, install and run picasa.
ar x picasa_2.7.3736-15_i386.deb data.tar.gz
mkdir -p ~/bin/google/picasa
mv data.tar.gz ~/bin/google/picasa
tar zxf data.tar.gz
rm -f data.tar.gz
ln -s google/picasa/opt/picasa/bin/picasa
So going through the lines:
* I used wget to download the latest 32bit deb of picasa.
* I then used ar to extract the install files from the deb.
* I created a directory and all it's parent dirs to place picasa (~/bin/google/picasa).
* I moved the archive to the above dir.
* I changed to that directory.
* I extracted the archive.
* I deleted the archive.
* I changed dir to ~/bin.
* I created a symbolic link so that I could run ~/bin/picasa to execute the program.
* I ran picasa.
Hope that clears things up for you.