If you are using the GD Home Page as your home page, you can add widgets to any of the GD Home widget areas, and you can add content on the page too, with or without shortcodes:
https://wpgeodirectory.com/docs/layout/#directory
https://wpgeodirectory.com/docs/core-shortcodes/
If you are using a normal WP page as your homepage, then it depends on the widget areas given by the theme, and you can add content to the page using shortcodes.
So you would add a GD Home Map widget or this shortcode: https://wpgeodirectory.com/docs/core-shortcodes/#locationmap
For the search, you would add the GD Search widget or this shortcode: https://wpgeodirectory.com/docs/core-shortcodes/#search
If you want to search by categories, review https://wpgeodirectory.com/docs/gd-search/
To add listings, add the Popular Post widgets or this shortcode: https://wpgeodirectory.com/docs/core-shortcodes/#poppost
Thanks