I want to put files on my Arch Linux file server so that others can download them via HTTP. Where under
/var should they be placed?
Mostly it's /var/www but it depends on your webserver and the configuration.
Check what web server software you have installed. The default on most distros will be apache, but again like most distributions ArchLinux also supplies
nginxso it depends on which one you picked.
Check the config files of the installed server software. This will likely be in
/etc/lighttpddepending on 1).
Somewhere in said configuration there will be a header stating the default document root for the default host. As @Rainer pointed out,
/var/wwwis the most commonly used standard location, but it never hurts to make sure. Homework for this step: Lighttpd docs, NginX docs, Apache docs depending on which software you installed