Download the zip file from the Tomcat site and unzip the folder with its whole content, preferably on the root directory (can be anywhere).
Go to the bin folder from terminal and execute the following lines.
To make the sh files executable in the bin folder
$ chmod +x .sh
to start the server
to stop the server
By default Tomcat runs in the port 8080. To verify if it is running correctly then in terminal execute
$ sudo lsof -i :8080