Router setup
Home Assistant OS and its Add-ons (like VPN or DNS server) require changes to your local network. Most home routers should support these, although each brand's user interface and feature-set are different. Due to this, I'll only be able to give a bit of guidance on what needs to be set.
I'm going to base this guide on a router running OpenWrt, an open-source Linux-based operating system primarily used on embedded devices to route network traffic. OpenWrt replaces the factory firmware and provides a unified user interface, third-party package management, and a set of advanced routing features to a wide range of devices. Check out the list of supported devices in the OpenWrt Table of Hardware if you would like to install it too.