I don’t have a particular guide to reocmmend, but assuming you have a VPS already, you’ll basically need just a few components:
A VPN (I’d use wireguard) tunnel between your network at home and the VPS
A reverse proxy on your VPS (nginx-reverse-proxy is a pretty user-friendly implementation) to forward traffic to the correct host on your local network
A DNS record for your subdomain that points to your VPS’s public IP address.
That should basically do what you need. The reverse proxy will see the domain (whatever.example.com) and pass it on to the machine on your local network (e.g. 192.168.1.111:8888) via a VPN connection (which will push the routes so the VPS knows how to get to your local network).