To send a communication to the mobile app you will follow the same process as creating a Campaign.
There is no separate delivery method for sending to the mobile app. If a campaign is sent via Email or SMS it will automatically send to the mobile app as well.
If you want to send a campaign to the mobile app only, simply uncheck the Email and SMS option, the Send button will still be available to select and the communication will only be sent via mobile app.
Points to Note
If Email and SMS sending are turned off the checkboxes will no longer appear. The Send button will be the only option and the communication will be sent to the mobile app.