1. Install tomcat6 via synaptic.
sudo apt-get tomcat6 tomcat6-admin
There may be some tweaks that you need to do after install. I didn't need to change anything, but you can find help from the ubuntu help page for tomcat.
2. Download the turnkey version of BlazeDS from Adobe. The turnkey version comes with a preintegrated version of tomcat which we won't need. All that we need are blazeds.war, samples.war, and ds-console.war. Unzip the file. You'll find the files you need in the root of the directory.
3. Copy the files above to /var/lib/tomcat6/webapps/
cp *.war /var/lib/tomcat6/webapps
4. Restart tomcat. This will install BlazeDS.
sudo /etc/init.d/tomcat6 restart
5. Try hitting http://localhost:8080/ds-samples/