I already explained it how you can publish Android apps the easiest way with Visual Studio and Xamarin Android 7. Publish apps to the app store is similar than publishing apps to the play store.
Create the archive
In the context menu on the IOS project there is an option „create archive“ which starts the archiving process. Make sure that you have set the configuration to debug.
After the build is completed, the overview of all created archives is shown. The same window also appears when „view archives“ in the context menu is clicked.
Sign and Distribute
By clicking sign and distribute, the archive can be published. Next to app store deployment, you can choose enterprise or adhoc deployment. For enterprise development you need an enterprise developer account. After selecting the appropriate option, you have to choose the correct provisioning profile. After creating the .ipa file you have to upload your application to the app store via Application Loader. There is right no no other option correctly than this tool, because there is no web portal or similar like in the Google Play Store to upload your .ipa file.
Next to the way above, there is also another way to create the .ipa file. By setting the configuration to adhoc and change some settings or change the release configuration so that an .ipa file is created. This could be interesting for you if you use Visual Studio or if you want to integrate it into your build process.