You should try to use your distro's package manager to install tomcat. Or you can download a precompiled binary from here
Extract the binary (for example in /opt/apache-tomcat-x.y.z) and use /opt/apache-tomcat-x.y.z/bin/startup.sh to start it.
By default tomcat listens on port 8080, so if you want to change that port number, open /opt/apache-tomcat-x.y.z/conf/server.xml with your favorite editor and change the following line accordingly:
<Connector port="8080" protocol="HTTP/1.1" ...