Once you download Tomcat and extract the files from the zip there are a couple of things you need to do from a terminal in the tomcat/bin folder:
chmod 755 *.sh
You might also want to delete the *.bat files because you cannot use them anyway:
rm *.bat
There is also a nice shell script in the link above that will let you start and stop tomcat by typing in 'tomcat start' or 'tomcat stop' from a terminal window.