Before starting you need the Java Development Kit (JDK) and not Java Runtime Environment (JRE). Download it from http://java.sun.com as a .bin file and install it on your system or use the command:

sudo apt-get install sun-java5-jdk

Then set the Java Runtime variable

$ export JAVA_HOME=?Your java path?
$ export PATH=$PATH:$JAVA_HOME /bin

e.g. on Dapper

$ export JAVA_HOME=/usr/lib/jvm/java-1.5.0-sun-1.5.0.06

Now use the following command to install Tomcat

$ sudo aptitude install tomcat5 tomcat5-admin tomcat5-webapps

To Start, Stop and Restart the server

$ sudo /etc/init.d/tomcat5 start
$ sudo /etc/init.d/tomcat5 stop
$ sudo /etc/init.d/tomcat5 restart

You can access the root directory via port 8180 and the server listens to the address 127.0.0.1 So type 127.0.0.1:8180 in your web browser to access the server.