For a newbee rpm installation is good and easy.Install from rpm and if you want to use it with apache (for creating VirtualHosts) Install apache before tomcat and also download the file called mod_jk.so from apache.org.place that in your apache directory.
After install tomcat(only tomcat without apache) Place your files in $TOMCATHOME/webapps/.then access your files from localhost/file.set your TOMCATHOME in /etc/profile. This is just in brief.Why don't you read the README file.
Basically tomcat is a normal java application and it will run if you have the JDK installed and configured. Just download the zip file you need, extract the files from it, set the env. variables TOMCAT_HOME and JAVA_HOME and run with the shell scripts in the tomcat bin directory - that should be all.