here are a few hints to get you started:

• you need to change your /etc/apt/sources.list so it does include the non-free repository,
  so it will look like that:
  

  deb http://ftp.at.debian.org/debian/ lenny main non-free contrib
  deb http://security.debian.org/ lenny/updates main non-free contrib

• now run:
  

  aptitude update;
  aptitude install sun-java6-jre sun-java6-jdk

  for production systems you might want to use Java 5 JRE instead:
  

  aptitude install sun-java5-jre sun-java5-jdk

• now you need to tell your system, that you want to use the just installed JRE version:
  

  update-alternatives --config java
  update-alternatives --config javac

• check if it has worked out:
  

  java -version
  javac -version

• now you need to add JAVA_HOME to your bash enviroment:
  edit /etc/bash.bashrc and add:
  

  export JAVA_HOME=/usr/lib/jvm/java-6-sun/

  or if you installed Java 5 JRE:
  

  export JAVA_HOME=/usr/lib/jvm/java-5-sun/

• log out and login to your system again, or run the relevant above command

• apt-get install tomcat5.5 tomcat5.5-admin tomcat5.5-webapps

• you can try if Tomcat is working, by connecting from your server to http://localhost:8180
  the login credentials are stored here: $TOMCAT_HOME/etc/tomcat-users.xml

enjoy!