In many Android apps there is an option where you see three white lines in the top left of the toolbar, which indicates that if you click it, or pull the screen from the left, an extra menu slides out with more options. What is the name of this type of menu so I can look up how it is done?
This is Navigation Drawer which you want. Follow this tutorial to implement this type of functionality in your app
https://developer.android.com/training/implementing-navigation/nav-drawer.html