For a particular repo to get the alerts you will have to create a Webhook
Then to add new repo alerts you would need to create new WebHook Handlers with a path and a secret refer App.js for more info.
To Manage the Destination of the events, you would need a unique chat id of the group/private conversation by adding your Bot that you created with the help of @BotFather.
After obtaining the chat id, you can just pass it in sendMessage method of the bot along with the message and you will start getting the alerts.