DAViCal is a server implementing the CalDAV protocol. It's solely a server, with minimal direct user interaction, instead relying on using CalDav clients, such as Apple's iCal.app, Thunderbird with Sunbird, or Evolution.
DAViCal is written in PHP and uses the PostgreSQL database as it's backend to store the calendar information. Currently it only supports PostgreSQL, but there is work to support other databases as well.
pacman -S postgresql php php-pgsql
DAViCal is a web application, and therefore you need a web server set up as well. For this page, Nginx will be assumed, but DAViCal can run on nearly any web server. (Some may stop processing requests when they see the CalDAV HTTP headers, and therefore DAViCal will not be able to see them.)