Make sure you've activated the Vamtam Push Menu plugin:
If you don't see the plugin, please go to Appearance > Required plugins > install and/or activate Vamtam Push Menu
Make sure you are running Vamtam Push Menu version 2.07 or higher. In case you are running an old plugin version please follow this guide to update:
How to update the theme and bundled plugins (points #2 and #4 for the bundled plugins as Vamtam Push Menu)
Make sure there is a menu selected for the mobile menu location called "push menu".
Go to Appearance > Menus > Manage Locations > Push menu > select a menu from the drop down.
If you've done all previous steps and it still doesn't work, please check the value of VamTam > Layout > Header > Mobile Header > Enable Below. If it is set too low, the menu is never actually enabled - set it to a more appropriate value in order to resolve the issue.
If you've done all previous steps and it still doesn't work, please deactivate all plugins that don't come with the theme to rule out any third party conflicts.
For more information about the Mobile menu (Vamtam Push Menu plugin) please check this article: http://support.vamtam.com/support/solutions/articles/205539