I had a heck of a time getting this to work, and this is just as much for my notes as it is for the wider web world’s usage.
To use the pretty links of WordPress, I had to enable mod_rewrite in Apache. Which was actually already enabled with my default installation.
I was using virtual hosts in the /etc/httpd/conf.d directory, so I made sure that the <Directory> configuration included these lines:
Allow from all
Also I made sure that that virtual host itself had these options set:
Options Includes MultiViews -Indexes FollowSymLinks SymLinksIfOwnerMatch
But to my deepest chagrin, it still wasn’t working. After laying my head down on my desk and allowing the tears to flow like a mountain spring, I girded up my loins and looked again.
In Apache’s main config file, /etc/httpd/conf/httpd.conf I found an AllowOverride None line! NO! I was beat by my own laziness and ignorance again. I commented out that line, and pretty links suddenly worked.
Learn from my mistakes, Future Dewey/World at Large. Don’t let it fool you again.