In order to receive Push messages in your own app, you will need to install the SDK available for iOS and Android in your app. Before this will start to work, you need to generate a Push certificate for iOS or register your App in the Google Developer Console.
With the Push credentials you can add your App to the App Manager by giving your App a name and choose the desired messaging type.
You can choose from:
Default messaging: for bulk, marketing etc. Messages have unlimited lifetime (as long as the telecom or Push service provides)
OTP: One Time Passwords, high priority routing, message lifetime is 1 minute. If the Push does not arrive and you manually decide to send an SMS in stead, the Push message will be terminated to avoid double messages.
Critical: Use this in case the messages are of extreme high priority. When a Push message is sent to the user and the user does not respond to this (does not open the app) the system will automatically fall back on SMS after 30 seconds to ensure the message is being delivered. This might result in double messages. (receiving both SMS and Push)
Read more about how to generate your Push credentials:
How do I create a Push certificate for iOS?
How do I get my Android Server API Key?