A. Go to Settings > Notifications > [App Name] and ensure that 'Allow Notifications' is turned on. Check that the alert style is set to 'Banners' or 'Alerts' and that 'Show Previews' is set to 'Always' or 'When Unlocked'.
B. Make sure that your device is not in Do Not Disturb mode. You can check this in Settings > Do Not Disturb.