Sure thing.

So there are two parts to all of this:

1. Getting MediaWiki set up , properly configured and running.
2. Having it securely accessible from the Internet (if needed), including SSL certificates.

Part 1 is well covered my the MediaWiki release already. You only need to worry about the correct configuration. When you download the current version from the official MediaWiki page, you'll notice that there is already a docker-compose.yml file in there. This gets you most of the way to your destination.

Read the file and set the values of all variables you wish to override in a separate ".env" file in the same folder. It could look something like this:

MW_SCRIPT_PATH=/w
MW_SERVER=https://your-url.com
MW_DOCKER_PORT=80
MEDIAWIKI_USER=Admin
MEDIAWIKI_PASSWORD=some_password
XDEBUG_CONFIG=
XDEBUG_ENABLE=true
XHPROF_ENABLE=true
MW_DOCKER_UID=1000
MW_DOCKER_GID=1000

Now you can just docker-compose up and everything will be set up when visiting your site for the first time, it should hold your hand, guide you through configuration options and finally offer you to download the LocalSettings.php file, that contains all the decisions you've made. You can review and adjust it futher and finally save it to the same folder as your docker-compose.yml file. Refresh the site and it should be accessible right away. I would say for a closed audience, these are the most important options to set:

# The following permissions were set based on your choice in the installer
$wgGroupPermissions['*']['createaccount'] = false;
$wgGroupPermissions['*']['edit'] = false;
$wgGroupPermissions['*']['read'] = false;

These options will prevent people from creating their own accounts (you will have to create one for them from the UI) and it will block people from viewing any pages without being logged in.

If you do not wish to use SQlite but rather a dedicated DBMS (I strongle discourage you from getting into that trouble for smaller or even medium user bases), you will find more information on the page for alternative configuration recipes.

If you would like to go into part 2, just ask and I'll give you an overview of my setup here as well. I'm using docker-letsencrypt-nginx-proxy-companion.