OS X Server is now available free of charge for members of Apple's iOS Developer Program, so I have it installed on most of my machines. Unfortunately, having OS X Server installed complicates the use of the built-in local Apache web server which I use for web development. I've figured out how to make things work the way I like, and I have written this article so that I can find the information again when I need it. Maybe it will help somebody else too.
Enabling Local Websites
First, to enable the web server, open the OS X Server app, select Websites in the sidebar, and flip the switch to On. You should be able to visit http://localhost/ in a web browser and see a page titled "Welcome to OS X Server".
While you are on the Websites configuration screen, you may want to enable PHP and Python web applications.
If you have the Xcode service enabled, then instead of "Welcome to OS X Server" you may see the Xcode Bots page. This may be OK with you, but if you would rather not see the Xcode stuff in place of the default website, then in the Server app, go to the Websites screen, double-click Server Website to edit it, click the Edit... button next to Index Files, and remove the /xcode entry. Now, visiting http://localhost/ should take you to the "Welcome to OS X Server" screen, and you can visit http://localhost/xcode to see Xcode Bots.
Website Directories
Next, you need to know where you can put your website files so that they will be served by the server. By default, the server will look for files in /Library/Server/Web/Data/Sites/Default. You could put your files in that directory, but I prefer to use symlinks so that I can keep all my files in my home directory. So, for example, if your main website file is /Users/kdj/work/mywebapp/index.html, you can symlink it like this:
ln -s /Users/kdj/work/mywebapp /Library/Server/Web/Data/Sites/Default/mywebapp
Then if you visit http://localhost/mywebapp, you should see your website.
Per-user Website Directories
Alternatively, instead of making modifications to the /Library/Server/Web/Data/Sites directory, you might want to set up per-user websites as are available on OS X when Server is not installed and "Web Sharing" is enabled. To do this, you have to edit the https_server_app.conf configuration file. This file is only writable by root by default, so you will need to use sudo. So, for example, if you use vi, then do this to edit the file:
sudo vi /Library/Server/Web/Config/apache2/httpd_server_app.conf
You need to uncomment two lines. First, uncomment the line for apple_userdir_module to enable it:
#Server-specific modules
# SERVER_INSTALL_PATH_PREFIX should be set as Environment variable in launchd.plist
LoadModule apple_userdir_module ${SERVER_INSTALL_PATH_PREFIX}/usr/libexec/apache2/mod_userdir_apple.so
Then uncomment the line that includes the user configurations:
# User home directories
Include /private/etc/apache2/extra/httpd-userdir.conf
Then, after stopping and restarting the Websites service, you should be able to access directories under your ~/Sites directory. For example, if your user account name is kdj, and you have a website at /Users/kdj/Sites/mywebapp/index.html, then you should be able to visit http://localhost/~kdj/mywebapp.
MAMP
If you want to quickly set up an Apache/MySQL/PHP/Perl/Python stack, then check out MAMP as an alternative to using the built-in Apache server.
Credits
Thanks to Pascal Qyy for providing an Ask Different answer that was helpful.