Steps you need to follow in order to publish your app to App Store, after making sure you already did everything described in "Rebrand" section:
1. Go to Apple Developer Account -> Certificates, Identifiers and Profiles and create two new iOS certificates, one for Distribution and one for iOS Development. In the meantime you will be instructed to supply Certificate Signing Requests file and how to create this .csr file is also written there. After creating the certificates, download them and double tap .cer files to install them.
2. In Apple Developer Account, go to App IDs and create new one, ideally wildcard if you want to publish multiple apps in the future, so something like com.newapp.*
3. In Apple Developer Account, go to Provisioning Profiles and create one for Development and one for Distribution, selecting Certificate and App ID you prevoiusly set up. Good practice is to include type of profile (dist/dev) and dates in their names, so that after they expire and you will have to create new ones you won't be confused. If selecting your device will be required in one of the steps, you will have to set it up in Devices section. After creating the provisioning profiles download them and double tap to install.
4. Go to Itunes Connect, My Apps and create new iOS App.
5. After that your apple accounts are set, go to Visual Studio and connect to Mac (plenty of instruction on the Web).
6. Right click on Xamarin.iOS native project and go to properties, then to iOS Bundle Signing. Provisioning profiles should be automatically downloaded from your Mac. If they are not set corretly by default, set them manually.
7. Rebuild your app, select Ad-Hoc and iPhone in build configurations. After its done (it might take a while), move .ipa file to your mac and upload it with Application Loader.
8. After that, everything is self explanatory, you just have to fill in App information in ITunes Connect, add screenshots and select your uploaded build and you are ready to submit your app to Apple Review. Once Apple Review accepts your app, it will be visible in App Store.