You can go to the Settings of your phone and select the Notifications option. There you can manage how every app sends you notifications, customizing vibration, sounds, and for some apps, specific settings for different conversations/notification types (i.e. e-mail VS calendar reminder on GMail, etc.).
In the Notifications menu, you have to tap the words of the notification category, and not the toggle switch, in order to get to the next menu where you should see a Sound option. If you select that, you can then customize the sounds.