How do I even install Discourse?

[Lilly]

What's the proper way to set up Discourse behind a reverse proxy?

if you expose a port/ip, all traffic for that port will be handled. The only issue you need to resolve is IP forwarding. So you need to customize NGINX to allow for the forwarded IP addresses so it does not look like all traffic is coming from 1 IP, there is a post here on meta covering that.