I just grabbed the tar.gz from http://getsongbird.com/ then did the following:
I always favour shoving apps like this in /opt/. Ubuntu never use it for anything, so it's just personal preference on my part to use it. You can untar it anywhere you like.
sudo mkdir Songbird/
sudo chown -R MYUSERNAME:MYUSERNAME Songbird/
sudo chmod -R g+w Songbird/
mv ~/Songbird_0.6_linux-i686.tar.gz .
tar zxvf Songbird_0.6_linux-i686.tar.gz
As it's an alpha, it's quite handy being able to see the errors in the terminal, though I've not had any show stopping issues yet. You can make a launcher in the usual way if you wish too. fyi the songbird icon for the launcher is in:
It makes a folder in ~/.songbird2 which contains all your local settings, I've not started hacking around in there yet though.