As of version 2.0.0, theming your menu has become really easy. You'll probably only need to change the background color for the menu (and maybe include the mmenu-theme-light.css file for lighter colors).
The menu on this page uses the default theme.
Click the menu-button in the header to open the menu and see for yourself how easy it is to customize your menu.
Want to change a bit more than just the colors? Try this customizer tool.