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/

You're done.