How to install Apache Tomcat in Ubuntu?
Look at the documentation, the answer is essentially:
sudo apt-get install tomcat7
If you want a per-user instance installation (easier for development when starting-and-stopping are desirable) you can install the tomcat7-user package and use the utilities it provides (eg tomcat7-instance-create). This is all stuff covered by the documentation.
Note: tomcat6 and tomcat6-user packages are also available. tomcat5 is no longer packaged or recommended.