First you need to install the latest version of java. Then download the tomcat from apache site. create a user tomcat. unzip the tomcat zip file to the tomcat user home directory it will be likr /home/tomcat/tomcat. Now you have to set the env variables. in .bash_profile of the tomcat user. add the following lines
now you can start tomcat
To start tomcat go to /home/tomcat/tomcat/conf/catlina.sh
if ur setup is fine your telnet to port 8080 should connect you there. and if you browse http://localhost:8080
you should get the default tomcat page.
Thanks and Regards