I am currently using Collector with Portal. You have to have your Portal account set up first. Load all your data and create your map. Then download the Collector app onto your mobile device (in my case IPad) by going here: Collector for ArcGIS | ArcGIS . Once the app is downloaded, set it up and use the option for Portal when it asks for your credentials. Use your Portal login and url. Collector should then open and you should see the map you created in Portal on your Collector maps screen. Click on the map to open it.
Check out this page for more information: Create and share a map for data collection—Collector for ArcGIS | ArcGIS
If your Portal for ArcGIS is only accessible on your internal network, you will need to have your mobile device connected to the internal network as well. Another option would be to open ports so that your Portal instance is externally accessible. However, if you are going to go the latter, it may be easier to use ArcGIS Online.
My url looks like yours but without the home: "https://myserver.domain.com/arcgis"
As Jake said, the mobile devices used are connected to the internal network since my Portal is only accessible on the internal network.