So there are two ways to change your Notification tones. If you want to change the default Notification tone throughout the whole system, go to Settings>Sound>Notifications. But if you want different notification tones for email, text, etc., then you need to do what I suggested above. For example, open the Messaging app, tap the Menu button (which is the 3 vertical dot button on the screen), then Settings, then look for the Notification options for the Messaging app. You can change the tone to something else, which will make the notifications from text messages sound different from the default tone you had set in the system settings. You can do the same in the Email app.
The button you're referring to is the Recent Apps button. For Android devices that don't have a capacitative Menu button, you should be able to see an onscreen menu button, which usually looks like 3 vertical dots, or 3 stacked horizontal lines.