You can change your apps' notifications in Settings -> Notifications on a per app basis. Tap on Notification Grouping at the bottom of any app that has notifications turned on and choose Automatic, By App or None.
iOS 12 introduces the ability to "tune" your notifications from the Notifications Center. Swiping left on an notification or a group of notifications will now bring up 3 options: Manage, View, Clear All. Tapping "Manage" gives you the option to deliver notifications quietly. Quiet notifications will still appear in the notification center but will not play a sound, appear on your Lock screen, or present a banner or badge icon.