Page-specific Secondary Menus

I want to implement functionality in my theme that would allow me to create a new menu in the WordPress Menu section and assign it, through the backend, to a specific page. This new menu does not replace any current menu– it just adds a new menu as specified.

To be specific, different pages of my website will have different menus assigned to them, but the primary menu will still be there, in the primary navigation section above the pages and their menus. How do I get started?