While this HOWTO doesn't cover step-by-step installation of the required software, I believe it should be mentioned.
Both Redhat Enterprise Linux and Fecora Core 3 come with RPM packages for installing Apache. All you need to do with these distributions is run the Add/Remove Applications application and select the packages you want under Web Server or install the RPMs directly from the distribution CDs.
For other distributions you can download the Apache source directly from the Apache HTTP Server Project page:
http://httpd.apache.org/
The latest Java Development Kit and installation instructions are available from the Sun Java web page:
http://java.sun.com/j2se/1.5.0/download.jsp
Apache Tomcat is available from the Apache Jakarta web page. Detailed installation instructions are available in my Linux Macromedia Flex on Tomcat-HOWTO:
http://members.cox.net/midian/howto/flex+tomcat.htm