In order to add widgets to any page you need to have a dynamic sidebar configured. Whether or not you have a dynamic sidebar that is visible from your home page depends on the theme.
If you don’t, you can initialize a new sidebar by using the register_sidebar() function in your functions.php file (http://codex.wordpress.org/Function_Reference/register_sidebar)
And then use the id of the sidebar in the dynamic_sidebar() function (http://codex.wordpress.org/Function_Reference/dynamic_sidebar) where you want the widget to appear on your homepage (home.php or index.php).
Then you just need to goto Appearance -> Widgets in the backend, and add your widget to your new sidebar.