How to Install Tomcat depends primarily on what OS you're using. On RPM and DEB based linux it's rather easy and straight forward, others like Slackware/Gentoo will be a bit more involved.
Most modern distros usually include Tomcat with the distribution, you may want to have a look there first.
What flavor/version of linux are you running ?
What version of Tomcat do you need to install ?
Remember, Tomcat is a java servlet and thus requires Java. Older versions of Tomcat require the full JDK, newer versions can get by with just the JRE.
Feel free to review the documentation on the Tomcat website. http://tomcat.apache.org/
The documentation here is rather good, make sure you read the FAQ section too.