If you are running PHP as an Apache module, you should have a line like this in httpd.conf:
AddType application/x-httpd-php .php3 .phtml .php
To process more types as PHP (.html, for example), add them to that line.
I don't know how to tell Apache to apply special handling to files that have no extensions. You might be able to create the appearance of that behavior with some fancy use of mod_rewrite.
A better place to ask might be Usenet comp.infosystems.www.servers.unix.