given your 80 and 443 ports are forwarded, and yoursite.com points to your external IP <docker-compose -f https-poc.yml up> will start the hello-world webserver and it will be available on yoursite.com via HTTPS

https-poc.yml

version: '2'

services:
  nginx-proxy:
    image: jwilder/nginx-proxy
    container_name: NginX_Proxy
    ports:
      - 80:80
      - 443:443
    networks:
      - nginxproxy
    volumes:
      - /var/run/docker.sock:/tmp/docker.sock:ro
      - /etc/nginx/vhost.d
      - /usr/share/nginx/html
      - /data/letsencrypt-nginx-proxy-companion/certs/:/etc/nginx/certs:ro
    labels:
      - "com.github.jrcs.letsencrypt_nginx_proxy_companion.nginx_proxy"

  letsencrypt-nginx-proxy-companion:
    image: jrcs/letsencrypt-nginx-proxy-companion
    container_name: letsencrypt-companion
    volumes_from:
      - nginx-proxy
    volumes:
      - /var/run/docker.sock:/var/run/docker.sock:ro
      - /data/letsencrypt-nginx-proxy-companion/certs/:/etc/nginx/certs:rw

  hello-world:
    image: tutum/hello-world
    container_name: tutum-hello-world
    environment:
      - VIRTUAL_HOST=yoursite.com,www.yoursite.com
      - LETSENCRYPT_HOST=yoursite.com,www.yoursite.com
      - LETSENCRYPT_EMAIL=youremail@gmail.com
    ports:
      - 8080:80
    networks:
      - nginxproxy

networks:
  nginxproxy: