How do you expose a Home Assistant on the internet?

If you want secure remote access, the easiest option is to use Home Assistant cloud by which you also support the founders of Home Assistant. Another option is to use TLS/SSL via the add-on Duck DNS integrating Let's Encrypt. To expose your instance to the internet, use a VPN, or an SSH tunnel.

What ports does Home Assistant use?

The basics: How the app talks to your Home Assistant​ 1.4 and listening on port 8123. If you use Home Assistant OS and haven't changed any of the defaults, Home Assistant will also be reachable at http://homeassistant.local:8123.