To receive notifications about new Telegram messages, you need to make sure they are enabled. Easiest way to do so and to exclude wrong custom settings is by going to Telegram Settings → Notifications and Sounds. Try to Reset Notification Settings at the bottom of the page.
- Make sure Google Play Services are installed on your phone. GCM (Google's mobile notification service) is part of Google Play Services and it enables the Telegram app to launch when it needs to show you notifications.
- If you have a battery optimizer / Task Manager / Task Killer or something installed of that kind: put Telegram on the list of allowed apps (whitelist). The detailed steps vary a lot depending on your device, here are a few examples.
- Android 5.0: If you press the volume button on Android Lollipop (5.x), you will see not only the current volume but also the three settings: NO, ALL and IMPORTANT. They represent three types of notifications, and the NO setting mutes all notifications — even if you put Telegram on your 'Important' list in the Android settings.
- Android (older than 5): When you're using an older Android device with little RAM, it may sometimes have issues with the notification service. This could lead Android to closing the service. If you think this is the case, regularly restarting the device could solve that issue.
- Android (older than 5): go to Settings → Notifications and Sounds. If the "Keep Alive" and "Background Connection" options are disabled, consider enabling both. This guarantees timely notifications, since Google's GCM isn't always reliable.
- Telegram Settings → Notifications and Sounds. Try to Reset Notification Settings at the bottom of the page.
- Go back to the home screen, double tap home button, swipe upwards on Telegram. This will close the App.
- Go to iOS Settings → Notifications → Telegram, disable notifications, Re-launch Telegram, go back to the phone settings and set alert style back to e.g. banners.(this will re-register you on Apple's push server and you will get notifications)
- Phone settings → Action Center → Telegram, make sure that notifications for Telegram are enabled.
- Telegram Settings → Notifications and Sounds → Reset Notifications.
- Shut down Telegram (long press on back arrow key, swipe downwards) and relaunch it.
PS: During the installation of Telegram, your system asked you to confirm push notifications. If you rejected, notifications won't work. You'll have to reinstall the app in order to enable them — sorry, but Windows Phone doesn't offer an alternative way. (Please note that secret chats will be lost on reinstall. Other chats are stored encrypted in the Telegram Cloud, so you will have them even when you reinstall Telegram.)
Issue persists? Try contacting the Telegram support volunteers via Telegram Settings → Ask a question.