We just installed Tomcat7 at work, and it rund great.
To install Tomcat 6, just unzip it with
tar -zxvf apache-tomcat-6.0.35.tar.gz. Then just press Ctrl+Alt+T on your keyboard to open Terminal. When it opens, switch to the directory were you unzipped, and run the command below.
To start as a service
sudo /etc/init.d/tomcat6 start
In case you want another way of installing tomcat, tust press Ctrl+Alt+T on your keyboard to open Terminal. When it opens, run the commands below.
sudo apt-cache search tomcat
sudo apt-get install tomcat6
sudo apt-get install tomcat6-admin