To map your containers to local ports you have to use the -p option of docker run or use docker compose.

nginx must have access to the ports 80 and 443 (http and https) of your server.

Then you can map your containers to some incrementing port numbers (80000, 80001, 80002, ...). With these ports, you can configure nginx.

Instead of publishing each port to the local machine you can also use dockers bridges and only publish the two ports for nginx.

PS: I found this short tutorial.

You can use Docker Swarm 1.12.0 or later. Then deploy Nginx at an upper layer and configure it to forward each domain name to the corresponding port.

From a NGINX standpoint, you need to define upstreams to let NGINX act as a proxy between the clients and your other containers

The basic idea is to define upstreams blocks, like

upstream service_foo {
    server 10.0.1.2:45678;
    server 10.0.1.3:54321;
    keepalive 8;
}

The important bits here are:

• service_foo is the name we'll use later in the config to identify this service. If you have multiple services, you have to define multiple upstreams.
• server SOME_IP:PORT; tells NGINX that this one of the endpoints for this service. You can have multiple, like here, 2 containers, with 2 IP and ports, can handle requests for this service. (Look at the documentation for stickiness, round-robin or other way to distribute the load)

How to populate those IPs (or internal DNS names) really depends on your service discovery (if you use Consul, then Consul template can help you, but there are millions way to do it)

Then you need to send requests coming to NGINX to those upstreams

In your server block, this would like (usually with many more options to define headers, ...)

server {
    listen 443 ssl;

    server_name         {{ DOMAIN }};
    # ... server options

    location ~ ^/api/foo {
        proxy_pass service_foo;
        proxy_set_header Host $http_host;
        proxy_set_header X-Real-IP $remote_addr;
        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
        proxy_set_header X-Forwarded-Proto $scheme;

        default_type application/json;

        # HTTP 1.1 support
        proxy_http_version 1.1;
        proxy_set_header Connection "";
    }
#... rest of config

The important bits here are:

• NGINX listen on port 443 (and I terminate the TLS connection here, and skip many ssl_* options. But after NGINX, I consider my VPC safe enough and let me services talk in plain HTTPtogether (although I'd love to do gRPC instead, but that's another story). This choice is up to you, depending on how many services and how much trust/risk you handle, to decide where the TLS should stop.
• I define a location (in fact I define many more, but one is good enough for the example) which handle everything starting with /api/foo (unless another location is more specific on that path). This is the 'public' route served by NGINX
• in this location block, I define a bunch of proxy headers (if you look at the many blog posts and tutorials, everything here is pretty standard)
• the core thing to answer your question is the proxy_pass service_foo; directive.

In the end, here's what happen with such setup:

• NGINX listens to incoming http request from the internet
• when a request matches the /api/foo.. route, NGINX will proxy it to the service_foo upstreams.
• to resolve the service_foo reference, NGINX looks at the matching upstream block and pick a server.
• when the server reply, the response goes back the same path directly to the client (i.e. you'll see the response status code in the NGINX logs)

The core problem usually goes around the service discovery and updates, to dynamically refresh the upstreams. If your services are not scaled-out/created/destroyed intenseively, this could be easier. As you scale, the service discovery component really becomes necessary.

Amongst the open-source reliable and easy solutions I really like, you can use

• Consul as the distributed service registry (and key-value store and distributed lock systems, it's such a useful tool!)
• gliderlabs's registrator to automatically update Consul service registry with any container which are created/destroyed on any port on any host (registrator listen for docker events to add/remove their name and ports)
• consul template to generate nginx config dynamically upon changes

Hope this helps